CN102160011B - Method and device for producing a mixture of constituents with constraints, especially with premixing - Google Patents

Abstract

The invention relates to a method and a device for controlling the production of a mixture of constituents, especially a mixture with premixing dead volumes. By correcting the matrices for calculating the mixing constituents used in the calculation of formulations, by introducing limits, order relationship and equality constraints, the drift observed in certain particular cases is avoided by implementing the method and improvements are made, on the one hand, to the diagnostic aid and the control of the estimate of the properties so as to limit the deviations from the actual quality of the constituents of the mixture and, on the other hand, to the speed of manufacture of the mixture and the robustness of the method. The method and the device according to the invention allow multi-variable feedback control by a dynamic observer allowing an estimate to be made in real time of the constituent properties of the mixture, said estimate being sufficient to guarantee the effectiveness of the feedback loop.

Description

Preparation has the method and apparatus of the multicomponent mixture of constraint condition, especially premixed

Technical field

The present invention relates to for controlling multicomponent mixture, especially there is the method and system of the preparation of the potpourri of premixed dead volume (dead volume).

More specifically, the present invention is applied to online (in line) and automatically regulates multicomponent mixture (e.g., such as oil mixture), and wherein prepared potpourri observes a series of specification or important parameter.In such applications, the often kind of product comprised in potpourri is to the series of characteristics of the final potpourri obtained or parameter generation effect.

Especially, the present invention is applied to the characteristic of wherein various component or parameter is unknown or the preparation of potpourri that may change during the preparation of potpourri.Especially, the potpourri of petroleum products has these aspects, but method and system of the present invention can be applied to the potpourri of other products (such as, as cement, paint etc.).

In all cases, object obtains the potpourri with predefined state or predefined formation (constitutional) parameter.These parameters are relevant to the physicochemical property of the potpourri that will obtain.Such as, when oil mixture, these parameters can be the sulfur content, its octane value etc. of potpourri.For cement admixture, such as, parameter will be lime content, silica ratio, ferro-aluminum ratio etc.

Background technology

Method and system well known in the prior art makes it possible to prepare potpourri online or in the closed loop mode, that is has the feedback of the information that the measuring instrument (on-line analysis device) that is positioned at mixing apparatus (mixer) downstream based on use in real time, continuously or is periodically measured.These method and systems are applied to the component stream from intermediate product container usually.

Typical feedback process uses the deviation between target set point and measured value.This exports to return feedback process.

Another kind of typical feedback process comprises the prediction correcting characteristic to potpourri or parameter by increasing item (term) to their, and described item is the result of the difference between measured value and the prediction be not corrected being carried out to first-order filtering (first-order filtering).

These typical feedback processes have on the potpourri that is applied in and exported by mixer instead of the defect be positioned on the component characteristic of mixer upstream.

The qualitative constraint condition of the potpourri that will be produced is considered in the adjustment used usually, and the constraint condition relevant to component feeding-passage (channel) (such as, homogeneous (homogeneity) constraint condition in the restriction (size of such as pump) relevant to hydraulic restriction condition, the ratio that calculates, itself and value must equal 1 on whole passage).They also allow total potpourri preparation output to be controlled.

The various specifications that known system and method has a potpourri are the shortcomings met by the function of comprehensive (integrated) of the potpourri in the storage container of potpourri (volume averaging or accumulation) characteristic, and described storage container is located immediately at mixer downstream.This is because be usually positioned at mixer outlet and measuring the characteristic of potpourri on the instantaneous potpourri of the upstream of the storage container of potpourri, these measure make it possible to obtain overall quality (from mixer out or enter the stream of container) estimation, described overall quality is the target carrying out in potpourri aggregative model or container aggregative model (will provide the definition of these patterns subsequently) regulating.

Although the method and system of these synthetic operations is very suitable for conventional hybrid region, (it has component containers, pipeline (flow-off) (that is the charging when consuming them) may be had, and for the storage container of potpourri), but they are not enough to the direct continuous print upstream flow for operating component, and not necessarily, the direct continuous print transmission of the potpourri prepared when not transmitting via storage container.

This is because described method and system depends on the quality of component, it may change, especially during the continuous upstream flow of component.

In addition, in the configuration that directly downstream is flowed continuously with potpourri, by considering that the volume of mixture existed in storage container corrects the component ratio of the potpourri obtained by known system.Thus, in storage container the potpourri of given volume preparation during, easily great changes will take place for the characteristic of potpourri, and this is can not be received when the directly continuously transmission of potpourri.

Another defect of known system and method is that they can not manage by optimal compromise solution the situation be difficult to carry out like a cork.That is, when not meeting one or more constraint condition, the solution obtained causes following potpourri: the deviation between itself and required specification can not correctly be controlled.

Traditional feedback method is also not enough to manage equipment synchronous for premixed upstream components, especially when serial and/or parallel multiple compounding operation.This is because this compounding operation is delayed in the flowing of specific components, described specific components needs to use large preparation limit (manufacturing margins) to meet the specification of potpourri in storage container, but it causes the unnecessary and excessive quality (overquality) of costliness.In addition, this shortage synchronously may cause impacting (vibration), causes the inappropriate stress of control assembly, may cause their too early wearing and tearing.

Finally, known method and system usually regulate component ratio on the one hand independently and regulate the injection of adjuvant to adjust the specification of potpourri according to the mode of decoupling on the other hand.This adjustment independence hampers the saving that expensive adjuvant injects.

Known method and system are also by considering to limit relevant (the pump size in the passage selected in the upstream and downstream of mixer) with hydraulic pressure and be correlated with the economic restriction height of (scheduling constraint) and low restriction condition control total output of mixer, output is particularly made to maximize, thus shortening preparation time, the simultaneously automatic changing down when carrying out active constraint to the applicability of calculated formula.

Summary of the invention

The object of this invention is to provide the method for the preparation controlling potpourri, and corresponding system, to make up these defects.

Particularly, control method according to the present invention provides the multivariate by means of Dynamic Observer to regulate feedback process, for estimating the component characteristic of potpourri in real time, is enough to the effect ensureing backfeed loop.Thus, although have a large amount of uncertainties in one side component characteristic, and on the other hand to hybrid processing also just part understanding, the desired characteristic of potpourri is ensured.

Applying in (FR2901894) before this, applicant details the method for the preparation of control n kind component mixture M, the method makes it possible to the ratio u of the component determining to comprise in potpourri to obtain m many predetermined properties y of potpourri, its value between predetermined minimum and max-thresholds and/or, m ' in them individual (wherein m '≤n-1) is substantially equal to predetermined target value, and described method comprises the following step:

I () is when moment t=0:

(1) matrix B of m many characteristic y representing n kind component is determined,

(2) fill a prescription from predetermined minimum and max-thresholds and/or from predetermined target value determination benchmark make the characteristic of potpourri between described predetermined threshold and/or, the m ' in them is individual equals described predetermined target value, as n-dimensional vector represent the ratio of the various components comprised in the composition of potpourri, wherein

(3) will fill a prescription be applied to component to prepare mixture M;

(ii) when moment t '=t+ Δ t:

(1) measure by being applied in the formula that previous instant calculates and the characteristic y of mixture M obtained _mes,

(2) correction matrix of the estimation representing component characteristic is derived thus

(3) u that newly fills a prescription is determined in the following manner: the characteristic of potpourri between described predetermined threshold and/or, the m ' in them is individual equals described predetermined target value,

(4) this new formula u is applied to component;

(iii) at moment t "=t '+Δ t time, repeat front step (ii) operation (1) extremely

(4); And

(iv) during the preparation of potpourri, step (iii) is repeated all the time.

Thus, when start time t=0, that such as provide based on the manufacturer by component or from laboratory test data determine matrix B ₀, the progressive updating when potpourri is produced subsequently.

Should be noted that and can revise predetermined minimum and max-thresholds during married operation, and predetermined target value.

This method has such advantage, namely upgrades the estimation of component characteristic, thus makes it possible to consider that change in whole time course in their characteristics is to keep the desired specification of potpourri.This new method makes it possible to find out (factor out) because of the inaccuracy in the layering of measuring error, defect/pollution, not exclusively homogenizing or container or the component characteristic caused by various component variability in time and uncertainty.Thus, this method can be advantageously utilised in the equipment of the direct upstream continuous stream with component.

But the estimator required in this method has some significant shortcomings, e.g., such as, need estimation sometimes with the actual component characteristic fallen far short.Especially, under some particular case not understanding component of mixture, the speed observing convergence process has fallen, or do not observe convergence even at all, thus cause estimated characteristic outside physical extent, it is zero or is even negative (it may cause controlling the change on the direction againsted one's expectation), and itself and reality are not inconsistent completely.This kind of phenomenon normally once in a while occur and of short duration, but there is prepared mixture quality difference or prepare the consequence longer than necessary time consuming time of potpourri, and in refinery, again must prepare them thus to form new potpourri, the specification of its characteristic conforms expection product.This in the time and make again these potpourris unit availability in cost very high.

The object of the invention is by improving on the one hand auxiliary diagnosis mode and to the control of characteristic estimation thus the robustness of the deviation of the actual mass of restriction and component of mixture and the preparation speed and this method that improve potpourri on the other hand improves this method.

First, method according to the present invention makes it possible to not only to be to provide and ensures newly to form the prediction in the mass space (space that the tolerance zone namely exported by required potpourri limits) of potpourri and the backfeed loop of convergence between measuring, thus ensures the success of actual mix.

Secondly, the drift observed method according to the present invention makes it possible to uncertain relative to residue in component the homogenizing of variable characteristic, the container (poor etc.) increases robustness.Which results in the better convergence in the mixing situation of some difficulty, or restrain faster, and the larger availability of the equipment of therefore shorter potpourri preparation time and the more voluminous thing of preparation.Thus, the preparation dirigibility of prepared amount or raising potpourri can be increased.

For this reason, applicant introduces matrix in step (ii) by introducing at least one correct operation of at least one constraint condition corresponding with restriction, ordinal relation and/or equality constraint correction.

These new constraint conditions (it can not may be defined in the computing interval of benchmark formula) are independently and depart from predetermined minimum and max-thresholds and the predetermined target value in definition for the purpose of potpourri to be prepared at the beginning.Such as, can or on base-material and component can up-to-date lab analysis based on or by reasoning known, manually input or carry out selectional restriction based on the scope that configures for given mixer.Definition of order relation conditionally can be carried out in conjunction with external key element (have or not there is the target of substantially mixing tendency).Or idiocratically cannot can add these constraint conditions (because the distribution of constraint condition can be flexibly and relevant to potpourri in question, it can not be fixing usually with regard to arranging the configuration of mixer in question) thus for the definition of given potpourri one by one.Thus, can by specify the restriction of minimum and maximum sulfur content or all base-materials or ordinal relation or depend on they sulfur content base-material between equation define the constraint condition of sulfur content; This makes it possible to the potpourri that Stationary liquid must be satisfied to obtain its specification to use the priority of base-material for other base-material one or more of.These restrictions, equation and/or ordinal relation constraint condition systematically act on all base-materials in the equivalence of one or more of base-materials or the whole time course of prioritizing selection of particular measurement or potpourri to be prepared.

By introducing these new constraint condition, the characteristic estimated can be used as the change on constituent mass instruction (independent of formula associated with it calculating with control mixing).The component characteristic estimated can be used as the diagnostic message independent of the control of mixer, and makes it possible to promote the understanding (detection of the component that quality is suspicious etc.) to used component.

Advantageously, by prepare the mode measuring process (ii) of the continuous coverage program on potpourri operation (1) period measured by admixture characteristic y _mes.Term " continuous coverage program " is understood to the measurement referring to perform continuously when its character allows, or removes a succession of sample and measurement done on these samples.

Transient measurement on these potpourris when potpourri is just formed makes it possible to the equipment being used for the method directly to transmit in a continuous manner potpourri.Then, the method is in momentary mode.

Method according to the present invention has such advantage, and namely it can operate with aggregative model, then measures and can accumulate or volume averaging in the container for preserving potpourri.It also may switch to momentary mode (or contrary) from aggregative model during potpourri preparation.

Such as, this switching manually can also be performed by operator, thus during mixing changes required shaping modes.

This switching can also automatically perform successively, such as, at the end of mixing, when reaching flow volume, and it is also conceivable to the residual volume that will be produced.This configuration is especially for ensureing the direct transmission by oil pipeline, or ensure the quality of whole bottom product on production line at mixer and when having between the container storing final products in a large number at line volume, the described container for storing final products is arranged in remote storage region.

Advantageously, the predetermined instant during potpourri preparation, measures one or more characteristic of component and upgrades the matrix representing component characteristic thus, can be upgraded by one or more characteristic measuring component, and do not need to reset the method.This makes it possible to the estimation of one or more characteristic improving this component.The speed upgraded can be idiocratically adjustable one by one for each component.

According to the present invention, correction matrix can be carried out by least one correct operation introducing at least one constraint condition corresponding with the equality constraint in restriction, ordinal relation and/or at least one characteristic this correct operation is present in being B ₀'s initial value amendment in, corresponding to following equation (1)

$\frac{d{\hat{B}}_j^t}{\mathrm{dt}}=-{\mathrm{\β}}_j\mathrm{Hu}(y_j-y_j^{\mathrm{mes}}),---\left(1\right)$

Wherein

● β _j(strict arithmetic number) is the constant arranging convergence time, allows one by one the speed of convergence that idiocratically differentiation (differentiated) is estimated.

● matrix H is positive definite symmetric matrices, has the object ensureing the normalization (normalization) considering measurement-prediction deviation, allows constituent mass prediction deviation to calculate, thus supplying method convergence property; And

● yes transposed matrix, wherein j is admixture characteristic index,

By replacing equation (1) with the equation corresponding with new adaptation rule and/or obtained by the interpolation of additive term δ amendment.

In other words, in order to correction matrix by equation (1) is replaced with differential equation corresponding to new adaptation rule in the hope of expect constraint condition progressive accordance integration and/or pass through to perform to having initial value B ₀(estimate by adaptation rule before this and may revise) estimated value add additive term δ and revise initial value (that is, B ₀), additive term δ is calculated by the optimization meeting expection constraint condition completely and obtains.

Term " adapts to rule " and is understood to that the differential equation (1) of the estimation of component characteristic managed by vial.So adaptation rule newly according to the present invention comprises the new differential equation replacing differential equation (1), or the amendment of the Section 2 of differential equation (1).

According to the first embodiment, replace matrix corresponding to equation (1) with the equation corresponding to new adaptation rule amendment can comprise the increase of the additional function of peer-to-peer (1) or it is by the replacement of another independent equations.

According to the first distortion, by initial equation (1) being replaced with the equation of the interpolation of the additional function comprising peer-to-peer (1) to matrix modify, that is:

$\frac{d{\hat{B}}_j^t}{\mathrm{dt}}={\mathrm{\β}}_j\mathrm{Hu}(y_j-y_j^{\mathrm{mes}})+\mathrm{\λf}\left({\hat{B}}_j^t\right)---\left(1.1\right)$

Wherein

● f is nonvanishing function, and the profile according at least one constraint condition corresponding to enable restriction with introducing, ordinal relation and/or equality constraint is selected;

● λ is weight coefficient, makes the return speed of estimated component characteristic can be adjusted by the tolerance interval limited; And

● H is that diagonal matrix is so that the convergence property of supplying method.

In order to ensure this system convergence, the various selections that will keep the matrix H of symmetry and positive definite are possible.

Such as, following matrix H may be used, which introduce the normalization coefficient based on initial baseline formula:

For finding out the physical proportions effect to another characteristic and the different changing sensitivities specific to each characteristic from a characteristic, the normalization particular importance of being undertaken by matrix H.

Then, this normalization allows the prediction deviation (after finding out proportional effect) calculated to be adjusted better, and such as, this adjustment may relative to benchmark formula, and the item be associated with current formulation is performed pro rata.

This constant β _jfor idiocratically distinguishing the speed of convergence of described estimation one by one, and make it possible to especially consider the special characteristic specific to the transfer delay of each characteristic.

As β _jthe example arranged, can adopt the value of 2 to 4 times that equal pure delay.

Such as, for the characteristic of such as relevant to the transfer delay of 10 minutes octane value, β will be set to 20 minutes.

Extract the characteristic of number percent (on-line chromatograph analysis) for such as relevant to the transfer delay of 40 minutes 70 DEG C, β can be set to 80 minutes.

By suitably choice function f so that the convergence property of keeping method is constant when introducing the constraint condition relevant with obtained estimation (limit, ordinal relation and/or inequality constrain condition).Thus, this function ensures asymptotic convergence, ensures to meet constraint condition at the end of convergence.

Nonvanishing function f can be selected according to the profile convergence of estimated component characteristic being pointed to the class value meeting at least one constraint condition corresponding with restriction, ordinal relation and/or equality constraint.

Or matrix computations can be used to select this function f according to piecewise linearity or logarithm profile.

In order to provide an example, can realize as minor function.

For restriction condition, thus this function f can adopt following form:

Consider comprise B (i), the inner interval [Bmin, Bmax] of non-NULL,

f(y)＝0 if y∈[Bmin，Bmax]

f(y)≤0 if y≥Bmax

f(y)≥0 if y≤Bmin。

For ordinal relation constraint condition, thus this function f can adopt following form:

Make m be the base-material quantity deferring to ordinal relation: Bj (1)≤...≤Bj (m).

Adapt to rule and can adopt following form:

Wherein λ >=0.

Wherein

$f\left({\hat{B}}_j\right)=\left(\begin{array}{c}{f}_0(B_j^{\min }-{\hat{B}}_j\left(1\right))\\ f_1({\hat{B}}_j\left(1\right)-{\hat{B}}_j\left(2\right))\\ .\\ .\\ .\\ f_{m-2}({\hat{B}}_j(m-2)-{\hat{B}}_j(m-1))\\ f_{m-1}({\hat{B}}_j(m-1)-{\hat{B}}_j\left(m\right))\\ \left(0\right)\end{array}\right)-\left(\begin{array}{c}{f}_1({\hat{B}}_j\left(1\right)-{\hat{B}}_j\left(2\right))\\ f_2({\hat{B}}_j\left(2\right)-{\hat{B}}_j\left(3\right))\\ .\\ .\\ .\\ f_{m-1}({\hat{B}}_j(m-1)-{\hat{B}}_j\left(m\right))\\ f_m({\hat{B}}_j\left(m\right)-B_j^{\max })\\ \left(0\right)\end{array}\right)$

With

$\∀i\∈\left[\right|1,m-1\left|\right],f_i\left(y\right):\left\{\begin{array}{cc}=0& \mathrm{ify}\≤0\\ \≥0& \mathrm{ify}\≥0\end{array}\right.$

For equality constraint, this function f can adopt following form, as H (normalization), A (to give a definition) and estimation B _jmatrix product:

The quantity of the sub-portfolio (subassemblies) (its characteristic j is identical) of component is represented by m.Such sub-portfolio is called as " one group of equation ".Introduce the following matrix A that size is n × n:

$A=\left(\begin{array}{c}{R}_1\\ .\\ .\\ .\\ R_m\\ \left(0\right)\end{array}\right)$

Wherein:

According to the second distortion, revise matrix by initial equation (1) being replaced with the equation corresponding with the realization of the new adaptation rule represented by following equation

Wherein δ t is window integral time (that is, the length in the time interval of taking the mean) and s is the time variable of integration.

Preferably, δ t is less than the renewal frequency of estimation.

Thus, equation (1.2) is used to determine the matrix corrected this makes it possible to integrate order in the past service time average (sliding time window).This system is preferably used in the situation about measuring once in a while of the characteristic of the product that blending ingredients obtains, and these characteristics are not refreshed in each computing interval.

According to the 3rd distortion, revise matrix by initial equation (1) being replaced with the equation corresponding with the realization of the new adaptation rule represented by following equation

Wherein δ t is window integral time, and Δ is transfer delay and s is the time variable of integration.

Time variable s be used for being operated in postpone sliding time window around Δ, width δ window on.

In the second embodiment of the present invention, revise matrix by adding additive term δ at least one in equation (1), (1.1), (1.2) or (1.3) and matrix corresponding following calculating:

${\hat{B}\mathrm{complete}}_j^t=({\hat{B}}_j^t+\mathrm{\δ})---\left(1.4\right)$

Wherein vectorial δ meets equation δ * u=0, makes prediction because of following equation constant (iso-prediction):

$y={\hat{B}}_j^t*u=({\hat{B}}_j^t+\mathrm{\δ})*u---\left(1.5\right)$

Next, replace the correction matrix in step of the present invention (ii)

Determine vectorial δ to ensure often systematically meeting in a flash the constraint condition on potpourri.Estimation for often kind of component idiocratically defines it one by one.Especially, this vector makes it possible to the exit of the system of viewed deviation profile between the laboratory measurement of component characteristic and the characteristic of these components estimated, this be distributed in input component completes and preferably towards stream row (flowing-draining) container etc. selected direction (such as according to new lab analysis) and do not damage the convergence property of method.

The scheme optimized under the calculating of δ can comprise direct algebraic manipulation or constraint condition.

According in order to calculate the selection that it does, vectorial δ is used for estimated characteristic to point to specific direction, e.g., and the value of the new lab analysis of such as component.This correction δ can also be used to the priority ranking in the restriction of the specific components of the container providing self-isolation, with come Artesian Drainage container (being always filled with the container of component) those compared with, its characteristic estimated must keep the laboratory reference analysis close to them, have and be disturbed and time dependent characteristic, and release estimating system is favourable for this reason.

The calculating of δ (except iso-prediction-constraint condition δ * u=0) can consider other constraint condition relevant with estimated component characteristic: the restriction in the equation of characteristic, characteristic, total or part order relation.The advantage of this system is in a flash in office and be not only meet these various constraint condition progressively.

According to equation (1.4) or at each iteration system ground or the matrix in mode with good conditionsi, the value of calculated δ being added into estimated component characteristic.

Consider the step (s) of premixed component before composition mixture, the formula u determined during the operation (3) according to the step (ii) of method of the present invention considers the delay caused due to the dead volume existed in the equipment in premixed region.

Thisly synchronously make it possible to improve the preparation of potpourri and meet the property settings value of potpourri.It also makes it possible to reduce preparation limit, and thus control group shunting more accurately, and prevent excessive quality.Finally, this control more accurately of component stream limits impact, and thus limits the inappropriate stress of device control unit.Larger robustness in this change synchronously additionally providing total output of mixer.

Advantageously, at correction matrix operation during, the variable U that the variable u of a use in the equation (1.1) used, (1.2), (1.3) and (1.4) is defined by formula vector U (t) of the dead volume considering moment t replaces, and makes:

U(t)＝(U ₁(t)，...U _n(t)) ^t

More specifically, at matrix amendment the first embodiment first distortion in, use following equation to determine it:

$\frac{d{\hat{B}}_j^t}{\mathrm{dt}}=-{\mathrm{\β}}_j\mathrm{HU}\left(t\right)(y_j\left(t\right)-y_j^{\mathrm{mes}}\left(t\right))+\mathrm{\λf}\left({\hat{B}}_j^t\right)---\left(2.1\right)$

Wherein, f and λ by reference to equation (1.1) and define, b _iit is the vector of the characteristic of component i.

At matrix amendment the first embodiment second distortion in, use following equation to determine it:

At matrix amendment the first embodiment the 3rd distortion in, use following equation to determine it:

Wherein δ t is window integral time, and Δ is transfer delay and s is the time variable of integration.

At matrix amendment the second embodiment in, vectorial δ meets equation δ * u=0, makes prediction because following equation and constant (iso-prediction):

$y={\hat{B}}_j^t*U=({\hat{B}}_j^t+\mathrm{\δ})*U---\left(2.5\right)$

Advantageously, the order synchronously comprised in this equation and export quantity to consider premixed delay and transfer delay.

This is because premixed region and analyser cause postponing.According to measured characteristic, analyser postpones to be taken as constant or variable, and this depends on measured value.Consider the corresponding measurement that will be provided by analyser current because analyze and postpone (it comprises delay in sampling circuit and analyser postpones) and unavailable, postpone to compensate these, synchro system is used, the future value (based on component feature and the last number percent calculated) of its prediction characteristic according to method of the present invention.

Such as, when variable measurement postpones, use the look-up table associated by some length of delays with given operating interval: the constant delay profile then obtaining segmentation, when opereating specification changes, delay class changes automatically.Then, what this delay class caused predicting with measurement is new synchronous.

Advantageously, in the control method in accordance with the present invention, determined formula u at the end of step (ii) is determined by the optimization process comprising series of steps, during the process of the optimization process of this series of steps, if be difficult to carry out about the whole issue of institute's Prescribed Properties, then seek the solution of the minimum problem relevant with the minimum number of precedence constraints, step-by-step increase the quantity of considered precedence constraints, until obtain the formula u of the precedence constraints representing maximum quantity.

Such as, these steps are as follows:

The determination of the solution of (a)-whole adjustment problem P0, this solution comprises the optimization of C/C composites u considering the constraint condition on component ratio and the constraint condition on admixture characteristic,

If-whole adjustment problem P0 can separate, then the solution of application formula u-P0;

B if ()-all adjustment problem P0 intangibilities, then determine that minimal adjustment problem P1 is by the formula u separated, it only considers the constraint condition be defined as on the problem P0 of precedence constraints; This problem P1 comprises a succession of normally feasible optimization problem, and its standard is the punishment to violating described precedence constraints, thus for the accessible new value of these precedence constraints definition;

If c ()-minimal adjustment problem P1 can separate, determine that adjustment problem P2 is by the described non-preferential constraint condition reaching new value and problem P0 of the precedence constraints of the formula u separated, its P0 that considers a problem; This problem P2 comprises optimization problem, and its standard is the punishment to violating described non-preferential constraint condition, thus for the accessible new value of these non-preferential constraint condition definition,

If-minimal adjustment problem P1 intangibility, application current formulation u (formula that is, applied before the optimization of step (ii));

If (d)-would regulate problem P2 to separate, determine that adjustment problem P3 is by the formula u separated, its described of non-preferential constraint condition describedly reaching new value, obtain in step (c) considering the precedence constraints of the problem P0 obtained in step (b) reaches new value and other non-preferential constraint conditions all less than the problem P0 by problem P1 and P2 process; This problem P3 comprises a succession of normally feasible optimization problem, and its standard is the punishment to violating other non-preferential constraint condition described, thus for the accessible new value of these other non-preferential constraint condition definition,

If-regulate problem P2 intangibility, then apply the formula obtained by problem P1; And

If e () regulates problem P3 to separate, then applied formula is the solution of problem P3, otherwise formula is the solution of problem P2.

Majorizing sequence (a) to (e) ensure that the optimum management of priority, makes it possible to by decomposing them to process the problem be difficult to carry out, thus obtains a series of feasible constraint condition.These majorizing sequences have such novelty, if namely whole issue is difficult to carry out, seek the solution of minimum problem, then increase the number of constraint condition step by step, instead of gradually reduce the number of constraint condition as in traditional majorizing sequence.Using such method, may obtain the formula u always meeting best and be defined as the constraint condition of precedence constraints.

Advantageously, relevant to benchmark by the non-preferential constraint condition of problem P2 process and be called as " adjustment " constraint condition corresponding with fixing set point adjustment equation.

Advantageously, as described below, step (b) and (d) self are the majorizing sequences that can be divided into multiple step.

Step (b) preferably comprises step (b _i), wherein process hard (preferentially) constraint condition of descending sort continuously.At each step (b _i) period, object is the best tension and relaxation (relaxation) of the value finding the whole hard constraint conditions providing same levels i, it becomes accessible constraint condition, reached constraint condition in the characteristic of the precedence constraints on consideration binder ratio and the potpourri of grade j > i, not necessarily at current procedures b _istep b before _iby tension and relaxation.

Step (d) preferably comprises step (d _i), wherein process soft (non-preferential) constraint condition of descending sort continuously.At each step (d _i) period, object is the best tension and relaxation of the value finding the whole soft-constraint conditions providing same levels i, it becomes accessible constraint condition, and the reached constraint condition in the characteristic of the potpourri of the precedence constraints on consideration binder ratio, hard grade is (not necessarily in step (b _i) by tension and relaxation), in the characteristic that regulates of the target that calculates in the step (c) according to regulating the reached constraint condition of target and last not necessarily at current procedures d _isteps d before _iby the reached soft-constraint condition in the characteristic of the grade j > i of tension and relaxation.

Advantageously, majorizing sequence can comprise additional step, therebetween, if can separate at front adjustment problem P3, consider step (b), (c) and (d) period determine describedly reach new value to determine that adjustment problem P0 is by the formula u separated.

Thus, the optimal anchor direction of calculated formula can be ensured, such as, by maximizing by the mode of hierarchical arrangement or minimizing specific components, or by minimize immediately when enough degree of freedom are available want calculated formula and initial baseline fill a prescription between deviation.

In some cases, although initial whole issue is difficult to carry out, this additional step makes the optimum orientation that still can obtain the formula relevant with the initializing constraint of all decomposeds.

Advantageously, the precedence constraints that solution problem P1 considers is the constraint condition on component ratio and the constraint condition on admixture characteristic.

Constraint condition on component ratio comprises the simple restriction on component ratio and the constraint condition in component ratio sum especially.Precedence constraints on admixture characteristic not necessarily P1 during front iteration by tension and relaxation.The solution expected be consider on admixture characteristic not necessarily by the formula u of the precedence constraints of relaxation.

If the method is intended to the equipment of the potpourri for the preparation of n kind component and adjuvant, for adjuvant to its influential admixture characteristic j, control model considers the effect d in the operation (2) of step (ii) and the adjuvant of (3) period interpolation according to following equation:

The invention still further relates to preparation and control the system of multicomponent mixture, it comprises: for transmitting the component of the wanting mixed transmission channel to main channel, described main channel is connected to the place receiving potpourri, for controlling the device of the flow velocity of component in each transmission channel, the device of the representative parameter of the potpourri be produced for continuous coverage in main channel, and for the device of the ratio that calculates the various components comprised in potpourri, be connected to the estimating apparatus of calculation element, described estimating apparatus comprises the programs device by using the measured value of the admixture characteristic measured by measurement mechanism to produce the estimation of component characteristic, calculation element comprises the programs device of the ratio being calculated the various components comprised in potpourri by the mode of this estimation, thus obtain the potpourri with predetermined properties, the system is characterized in that described estimating apparatus comprises for being introduced and restriction, at least one constraint condition corresponding to the equality constraint in ordinal relation and/or at least one characteristic is to correct the matrix according to the step (ii) of method of the present invention programs device.

" continuous measuring device " is understood to the device referring to realize test constantly process as defined above.

Advantageously, estimating apparatus comprises execution according to the step (i) of method of the present invention and the programs device of (ii), comprehensive additional external information, as the lab analysis of nearest component containers, stream row's container indicator and the container in tendency in (mix the maximization of potpourri/minimize) and the relative priority of mixing tendency target expected in application use target.

Advantageously, estimating apparatus comprises sequencing synchronous device, and it considers the delay that the dead volume in the region of at least two kinds of components of premixed mixture causes.

As change, estimating apparatus comprises sequencing synchronous device, the delay that the dead volume during its consideration is at different levels causes, and at least one-level comprises one or more region of at least two kinds of components of premixed mixture.

In other words, level is between the component no matter whether mixed flows into and to flow out with the component no matter whether mixed, and comprise at least one premixed (each in these components self may be the potpourri of component) that at least two kinds flow into components, transmit the premixed of these components as output.

Preferably, these synchronous devices are programmed the equation (2) of the operation (2) of step (ii) to implement a methodology in accordance with the present invention to prepare the potpourri of component, before preparing potpourri, wherein generate at least one premixed of at least two kinds of components.

Advantageously, described system comprises the optimizer being connected to calculation element and potpourri target storage, optimizer comprises the programs device of the formula u optimizing component ratio, and the described formula determined by calculation element is relevant to the potpourri target be stored in described memory storage.

Preferably, optimizer then comprises the programs device of the optimizer for realizing above-mentioned preparation method.

Advantageously, system comprises: at least one additive container being connected to main channel via transmission channel; Be positioned at the downstream in the region of blending ingredients, for controlling the device of the additive flow rate provided in transmission channel be associated with container; And be connected to the adjuvant injecting controller of described control device, optimizer and potpourri target storage, adjuvant injecting controller can consider the target that potpourri target storage provides, for adjuvant, its influential admixture characteristic j is optimized to the ratio of adjuvant, thus regulate the described individual features j of potpourri.

Accompanying drawing explanation

Now, the present invention will be described, in accompanying drawing by way of example and with reference to appended nonrestrictive accompanying drawing:

-Fig. 1 is the schematic diagram according to the system for the preparation of mix product of the present invention;

-Fig. 2 is the example of the topology (topography) of the potpourri of the 6 kinds of base-materials comprising three premixeds;

-Fig. 3 shows the example of the sequence of optimization problem;

-Fig. 4 shows the sulfur content of the potpourri of example 7 and the change of time correlation;

-Fig. 5 shows the binder ratio of the potpourri of example 7 and the change of time correlation;

(Fig. 6 a), and the change of the quality of the gasoline mixture of example 8 (namely RVP regulates (Fig. 6 b) and RON to regulate (Fig. 6 c) and extracts (Fig. 6 d) and the monitoring for the region of benzene content (Fig. 6 e) for number percent) and time correlation-Fig. 6 a-6e shows the change of binder ratio and time correlation;

-Fig. 7 a-7f illustrates the following parameters of gas-oil mixture and the change of time correlation, and described gas-oil mixture has the adjustment undertaken by the injection of the adjuvant of example 9:

Fig. 7 a: injection distribution (profile) affecting the drops of cetane rating,

Fig. 7 b: the injection distribution affecting filterable drops,

Fig. 7 c: the ratio of the base-material 1 and 3 used in the preparation of potpourri,

Fig. 7 d: the cetane rating of potpourri,

Fig. 7 e: the filtrability of potpourri, and

Fig. 7 f: the sulfur content of potpourri.

Fig. 8 represents the chart of the function f described in example 1.3.A;

Fig. 9 represents the sulphur property estimated at the estimating apparatus of front application used according to applicant;

Figure 10 represents the sulphur property using the estimating apparatus corrected by vectorial δ according to the present invention to estimate; And

Figure 11 and 12 represents the example of the topology used in example 2.1.

Embodiment

By in the situation of the oily equipment (oil plants) for the preparation of potpourri, the present invention is described below, described potpourri comprises both certainty ratios of multiple available base-material or component, thus the combination of these base-material characteristics allows potpourri have desired characteristic in accordance with extreme value or setting value.

Fig. 1 shows the figure of the system according to the preparation for controlling mix product of the present invention.

The component of potpourri or base-material are included in container 1,2,3, and for the ease of signal, its number is restricted to 3 kinds.Want mixed component to be sent to the main channel 7 providing mixer 8 along transmission channel 4,5,6, potpourri is transmitted to storage container 9 in main channel.The device represented by Reference numeral 10 in Fig. 1 is used for controlling the flow velocity of base-material in each transmission channel.Such as, they are flow conditioners of operation valve.

Analytical equipment 11, or continuous measuring device is used for measuring repeatedly the representative parameter of potpourri during the preparation of potpourri.Such as, these devices 11 comprise the in-line analyzer be connected with the mixer 8 being arranged in main channel 7.

When oil mixture, such as, the sulfur content (sulphur measurement), octane value (octane engine test (engine test)), cetane rating (test of hexadecane engine) etc. of potpourri measured by these analysers.

Described equipment also comprises the binder ratio comprised in calculating potpourri, and (formula device 12 u), determine optimizer 14 and the estimating apparatus 13 of binder ratio formula u, this formula will be sent to control device 10.

The effect of estimating apparatus 13 estimates base-material characteristic based on the analysis of the admixture characteristic completed by analytical equipment 11, calculation element 12 comprises the programs device being calculated the various binder ratio comprised in potpourri by the setting value of this estimation and these characteristics or the value of constraint condition that is associated with these characteristics, thus obtains the potpourri with predetermined properties.Calculate the binder ratio that will be employed repeatedly with not necessarily equal predetermined time interval (such as about 5 minutes), thus allow the characteristic accurately controlling potpourri.

Estimating apparatus 13 comprises the programs device for performing the operation determining component characteristic, and described operation forms above-mentioned according to the part preparing the method for potpourri of the present invention.

The effect of optimizer 14 is from the base-material characteristic estimated, the constraint condition from formula u and the constraint condition from admixture characteristic to optimize binder ratio formula u.Thus the formula u optimized can be used in operating control device 10.

Optimizer 14 comprises the programs device performing the method optimizing calculated formula, and described calculated formula is used for the execution according to the estimating apparatus of control method of the present invention.

In addition, described system comprises potpourri target storage 15.This potpourri target storage comprises the various targets arranged by user, to obtain the potpourri of expectation.It is connected to optimizer 14, thus for the target that each potpourri transmission is expected.

In this example, they are min/max constraint condition, the min/max desired orientation of component, the volume that prepare and the selected shaping modes (momentary mode that will define subsequently, aggregative model or container aggregative model) on the target of height in initial baseline formula, setting value type or characteristic and low restriction, component ratio.

The additive container 16 being connected to main channel 7 via transmission channel 17 can also be comprised according to system of the present invention, be positioned at the downstream of mixer 8.The device 10 controlling additive flow rate is also provided in transmission channel 17.This device 10 is driven (actuated) by the adjuvant injecting controller 18 being connected to optimizer 14 and potpourri target storage 15.

The formula that the drops from container 16 injects is optimized in the effect of adjuvant injecting controller 18, thus regulate particular characteristics concurrently with the optimization of the formula of the component 1 to 3 performed by optimizer 14, know following situation: if drops injection is saturated (such as, when reaching the predefined consumption restriction of user), the automatic switchover of drops control characteristic occurs on multivariate regulates by acting on component ratio, and this is controlled by optimizer 14.

Certainly, it is contemplated that multiple additive container 16.

Can operate according to two kinds of patterns according to system of the present invention:

-comprehensive analysis and Control (aggregative model)

This control is very suitable for the situation that potpourri flows into the final products container (storage container) of isolation.In the case, average quality comprehensive in whole container is controlled.

Then, control binder ratio, thus the temporal properties of amendment potpourri are to compensate the deviation in the mixture quality observed before this, thus make the characteristic of the whole potpourri comprised in storage container reach setting value, or within the scope of constraint condition.

Then, the volume controlling potpourri in the action of binder ratio and storage container increases simultaneously.

At this, distinguish between " potpourri is comprehensive " pattern and " container is comprehensive " pattern.A rear pattern considers volume bottom original container and quality before combination, otherwise the preparing product that " potpourri is comprehensive " pattern is flowing into from mixer operates, want the quality of this mix product controlled by comprehensively, that is, accumulation or on average when starting from mixing.

-transient analysis controls (momentary mode)

This control is very suitable for the situation that potpourri flows directly into oil pipeline, ship, train or truck.So, for good and all keep the instantaneous value of described analysis close to setting value or be important within the scope of constraint condition.In the case, the volume of action independent of the potpourri flowed into of binder ratio is controlled.

The operation of characteristic estimating apparatus 13 independent of selected shaping modes, no matter instantaneous or comprehensive pattern.In two kinds of patterns, the prediction of estimating apparatus all instantaneously and synchronously estimated performance, it then can use by optimised device 14.The optimizer that optimizer uses uses adjustment equation explained subsequently, it comprises setting value directly corresponding with expectation target in momentary mode, or the benchmark that the path adjusted by adjustable horizontal line (horizon) in aggregative model calculates.

Example 1.1 to 1.5,2.1,2.2 and 3 to 5 describes and can be used for realizing formula of the present invention.

These examples relate separately to following content: the feedback (example 1.1 to 1.5) not having premixed; There is the feedback (example 2.1 and 2.2) of premixed; Majorizing sequence (example 3); Management (example 4) in aggregative model; The adjustment (example 5) of adjuvant.

The feedback described in example 1.1 considers in-line analyzer, and this is the basis of Principles of Regulation.Especially, it uses the mechanism whether carrying out correction group intrinsic according to privileged direction (new lab of component characteristic analyzes) to estimate component characteristic in real time.

Example 1.1 to 1.5 be used for describing according to privileged direction introduce estimate the constraint condition (example 1.2 to 1.5) in characteristic and do not damage a series of concrete feedback scheme of the convergence property of whole system.

This feedback is added in example 2.1, thus when multiple premixed, allows the control synchronization of parallel (in peer) or serial (in multiple continuous premixed level).This allows to obtain more sane control in practice, because the impact of the vibration that this is less measured and any synchronous disappearance between predicting causes, and expands it for component premixed situation and uses.

Example 2.2 is similar to example 2.1, but corresponding to having the normalization of general topology of multiple premixeds and the concrete scheme of realization of mixer upstream.

Example 1.1 to 1.5 or the feedback process described in example 2.1,2.2 are used to the prediction calculating admixture characteristic.These predict the constraint condition equation that is used as in majorizing sequence, those described in example 3, and make it possible to calculate the suitable control for reaching the target arranged for potpourri.

Therefore, example 1.1 to 1.5 or 2.1,2.2 and example 3 to describe in momentary mode the example of required chain type process.

Example 4 makes it possible to provide specific supplemental (complement) by amendment threshold value (tension and relaxation of instantaneous constraint condition value) and amendment benchmark (setting value via reference path amendment) for the process in aggregative model, and it uses the principle of operation figure about the momentary mode described by example 1.1 to 1.5,2.1,2.2 and 3.

Example 5 describes the adjustment of being injected by adjuvant, its be increased to example 1.1 to 1.5 or 2.1,2.2 and example 3 mechanism in and it can use the similar mechanism of those mechanism to the aggregative model described in example 4.The principle switched to the adjustment of base-material y is described, the path of the mechanism that its mechanism corresponding to description from example 5 describes in example 1 to 3.

Example 6 describes various formulation optimization option.

When the potpourri of n kind base-material (or component), use following symbol:

● u (n-dimensional vector) be want calculated formula and it is benchmark formula.Formula represents the ratio of the various base-materials comprised in potpourri: u ∈ [0,1] ⁿand

● y (m dimensional vector) represents that m of the potpourri of formula u is estimated characteristic;

● the measured value of characterization j, has suppose linear hybrid rule.At this, can notice only when there is no premixed (dynamically or stable state, that is in instantaneous or equilibrium mode) and if there is premixed then applicable equations y=Bu in stable state;

● B is the m * n matrix of the component characteristic of potpourri; And

● the estimation of the B used in the calculation, according to mode.

The current properties y being positioned at the potpourri of mixer outlet is called as temporal properties.They are measured by in-line analyzer.

The current properties (being represented by z) having flowed into product is called as overall characteristic.

Current properties (being represented by zfb) for the storage container of potpourri is called as container bottom overall characteristic.

example 1.1: the feedback not having premixed, the control in momentary mode

The object of this example how shows equation (1) for realizing the operation (2) of the step (ii) of the method preparing and control potpourri, makes it possible to the estimation matrix calculating base-material characteristic.This example corresponds to direct mixed resin does not have the potpourri of premixed situation with preparation.

Based on u and measured value definition is used for upgrading following dynamic system:

$\frac{d{\hat{B}}_j^t}{\mathrm{dt}}=-{\mathrm{\β}}_j\mathrm{Hu}(y_j-y_j^{\mathrm{mes}}),---\left(1\right)$

Wherein

● matrix H is positive definite symmetric matrices and equals in this example:

● b _jtransposition, and

● β _jstrict arithmetic number,

Can explicit function it is the Lyapunov function of dynamic system (1).This is because it is just and the derivative of itself and time correlation is negative:

$\frac{\mathrm{d\ψ}}{\mathrm{dt}}=-{\mathrm{\β}}_j{(y_j-y_j^{\mathrm{mes}})}^2.$

Therefore, trend towards the maximum invariant arranged by dynamic system (1), be positioned at and { make d ψ/dt=0's in scope.Thus, trend towards making value, it is equal to and is defined as but, because the value of u is by constraint condition constraint, it can not be inferred and B _jequal.

But, when optimization problem comprises constraint condition and when solution exists, so gradually similarly, y is estimated _ion inequality constrain condition pass through measured value carry out associating (respect).

Thus, the use for the dynamic system (1) upgrading admixture characteristic constitutes feedback system, and it can avoid the skew between estimated value and measured value when exporting.

Variant in dynamic system (1) use can use initial baseline formula bias term e instead of formula u item in estimation differential equation.

When measurement is delayed by, and when postponing known, it is enough to synchronously measure u, y _jwith remain valid to make convergence property.

Except analyser transfer delay, the described component delay synchronously can considering mixer upstream.

Such as, as described below, observe this delay when premixed component.

example 1.2: the feedback returning estimation to nearest lab analysis

The estimation that can describe in example 1.1 add the correction term δ not affecting the end value of institute's prediction characteristic (iso-prediction).In this example, introduce these to correct to consider new laboratory measurement.

For each characteristic, refer to the new laboratory measurement of base-material.In order to calculate correction term δ, consider the minimization problem of following constraint:

Single constraint condition ensure that iso-predicts: lagrangian is used to solve this minimization problem clearly.The unique solution of this problem is:

${\mathrm{\δ}}_{\mathrm{sol}}={\stackrel{\‾}{B}}_j-{\hat{B}}_j-\frac{({\stackrel{\‾}{B}}_j-{\hat{B}}_j)u}{{\left|\right|u\left|\right|}^2}{u}^T$

In the ground of iteration system each time or this correction according to the condition test estimation matrix of applied component characteristic every now and then.

example 1.3: there is the feedback considering the constraint condition adapted in the estimation of rule

sub-example 1.3.A: limitation management

At this, we consider the one group of inequality constrain condition expecting the min/max type that the estimation matrix of component characteristic should be considered progressively.For each characteristic j, consider that non-NULL inside can accept interval (suppose the one group of actual value comprising component characteristic: wherein B _ji () represents vectorial B _ji-th component).It is also contemplated that make real output value f _j(X) there is the analytical function f of following characteristic _j:

f _j(x)＝0 $\mathrm{ifx}\∈[B_j^{\min },B_j^{\max }]$

f _j(x)≤0 $\mathrm{ifx}\≥B_j^{\max }$

f _j(x)≥0 $\mathrm{ifx}\≤B_j^{\min }$

Corresponding to real output value X.

Then, differential equation (1.11) is considered:

Wherein f is column vector, and its coordinate (be i-th at this) can be written as

This equation (1.11) corresponds to the equation (1.1) described when weight coefficient λ equals 1 above.

Therefore, for any starting condition, the solution of differential equation (1.11) restrains towards such as next part in time progressively:

$\{{\hat{B}}_j\left(i\right)\∈[B_j^{\min },B_j^{\max }],\∀i\∈\{\mathrm{base\; space}\},{\hat{B}}_{j}u=B_{j}u\}$

Convergence is completed by following Lyapunov function:

$\mathrm{\Ψ}\left({\hat{B}}_j\right)=\frac{1}{2}({\hat{B}}_j-B_j)H^{-1}{({\hat{B}}_j-B_j)}^T$

●Ψ(B _j)＝0

● for ${\hat{B}}_j\≠B_j,$ $\mathrm{\Ψ}\left({\hat{B}}_j\right)>0$

● $\frac{\mathrm{d\Ψ}}{\mathrm{dt}}=-{\mathrm{\β}}_j{({\hat{y}}_j-y_j)}^2+\mathrm{\λ}({\hat{B}}_j-B_j)H^{-1}f{\left({\hat{B}}_j\right)}^T\≤0$

By hypothesis, the coordinate i for all: and:

$\underset{\&OverBar;}{({\hat{B}}_j\left(i\right)-B_j\left(i\right))f\left({\hat{B}}_j\left(i\right)\right)=\left\{\begin{array}{cc}0& {\hat{B}}_j\left(i\right)\&Element;[B_j^{\min },B_j^{\max }]\\ \&le;0& {\hat{B}}_j\left(i\right)<B_j^{\max }\\ \&le;0& {\hat{B}}_j\left(i\right)>B_j^{\min }\end{array}\right.}$

Because matrix H is positive definite diagonal matrix, the solution of differential equation restrains on such as next part:

sub-example 1.3.B: equality constraint manages

At this, consider the one group of equality constraint expecting that the estimation matrix of component characteristic should be considered progressively.

The interpolation of additive term in differential equation

Differential equation (1.11) (wherein f should be selected as equaling 0) does not provide the identical evolution of equivalent base-material.

For each characteristic, when there are two prima faciess with base-material, solution based on:

Therefore

$b_1=b_2\&DoubleLeftRightArrow;\left(\begin{array}{ccc}-1& 1& \left(0\right)\\ 1& -1& \left(0\right)\end{array}\right)\left(\begin{array}{c}{b}_1\\ b_2\\ .\\ .\\ .\end{array}\right)\&le;0$

For three kinds of base-materials, obtain following equation similarly:

$b_1=b_2=b_3\&DoubleLeftRightArrow;\left\{\begin{array}{c}{b}_1-b_2=0\\ b_2-b_3=0\end{array}\right.\&DoubleLeftRightArrow;\left(\begin{array}{cccc}-1& 1& 0& \left(0\right)\\ 0& -1& 1& \left(0\right)\\ 1& 0& -1& \left(0\right)\end{array}\right)\left(\begin{array}{c}{b}_1\\ b_2\\ b_3\\ .\\ .\\ .\end{array}\right)=0$

Generally speaking, the sub-portfolio quantity (its characteristic j is identical) of component is represented by m.

Such sub-portfolio is designated as " one group of equation ".The component quantity be associated with one group of equation i is called as n _i, and note calculating N according to following equation _i,

Introduce the following matrix A that size is n × n: $A=\left(\begin{array}{c}{R}_1\\ .\\ .\\ .\\ R_m\\ \left(0\right)\end{array}\right)$

Wherein:

Each matrix R _isize be n _i× n.A is the diagonal matrix in units of block.

Consider new adaptation rule (1.12) of lower mask body:

$\frac{d{\hat{B}}_j^t}{\mathrm{dt}}=-{\mathrm{\&beta;}}_j\mathrm{Hu}({\hat{B}}_{j}u-y_j^{\mathrm{mes}})+\mathrm{\&lambda;HA}{\hat{B}}_j^t---\left(1.12\right)$

Wherein λ >=0.

Consider that k equals one group of equation of base-material (K >=1).Even if replace, still suppose to there is k the first base-material.Introducing based on size is the nonzero block of k × k and the square matrix A of n × n that defined by following equation _k:

Then, following equation can be written as:

$({\hat{B}}_j-B_j)A_k{\hat{B}}_j^T=-\frac{1}{2}[\underset{i=1}{\overset{k-1}{\mathrm{\&Sigma;}}}{({\hat{B}}_j(i+1)-{\hat{B}}_j\left(i\right))}^2+{({\hat{B}}_j\left(1\right)-{\hat{B}}_j\left(k\right))}^2]---\left(33\right)$

Consider following Lyapunov function:

$\mathrm{\&Psi;}\left({\hat{B}}_j\right)=\frac{1}{2}({\hat{B}}_j-B_j)H^{-1}{({\hat{B}}_j-B_j)}^T$

●Ψ(B _j)＝0

● for ${\hat{B}}_j\&NotEqual;B_j,$ $\mathrm{\&Psi;}\left({\hat{B}}_j\right)>0$

● $\frac{\mathrm{d\&Psi;}}{\mathrm{dt}}=-{\mathrm{\&beta;}}_j{({\hat{y}}_j-y_j)}^2+\mathrm{\&lambda;}({\hat{B}}_j-B_j)A{\hat{B}}_j^T\&le;0$

According to equation (33), we can write out:

$({\hat{B}}_j-B_j)A{\hat{B}}_j^T=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}({\hat{B}}_j-B_j)R_i{\hat{B}}_j^T$

$=-\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}[\left(\underset{k=1}{\overset{n_i-1}{\mathrm{\&Sigma;}}}{({\hat{B}}_j(N_i+k+1)-{\hat{B}}_j(N_i+k))}^2\right)+{({\hat{B}}_j(N_i+1)-{\hat{B}}_j(N_i+n_i))}^2]$

Therefore, the solution of differential equation restrains on such as next part:

$\left\{{\hat{B}}_j\right|\frac{\mathrm{d\&Psi;}}{\mathrm{dt}}=0\}=\{{\hat{B}}_j|{\hat{y}}_j=y_j\mathrm{et}\&ForAll;i\&Element;\{1,...,m\},\&ForAll;(k,l)\&Element;{\{N_i+1,...,N_{i+1}\}}^2,{\hat{B}}_j\left(k\right)={\hat{B}}_j\left(l\right)\}$

sub-example 1.3.C: ordinal relation manages

At this, consider the one group of ordinal relation expecting that the estimation matrix of component characteristic should be considered progressively.

For each characteristic j, consider the ordinal relation that (within the opereating specification that reorders) is relevant to m the first base-material under prerequisite without loss of generality.If m < n, then this ordinal relation be part, and if m=n, then this ordinal relation is whole, and n is the quantity of base-material.Therefore, this means: B _j(1)≤...≤B _j(m).

Consider m-1 the function with following characteristic:

$\&ForAll;i\&Element;\{1,...,m-1\},f_i\left(x\right):\left\{\begin{array}{cc}=0& \mathrm{six}\&le;0\\ \&GreaterEqual;0& \mathrm{six}\&GreaterEqual;0\end{array}\right.$

Represented the vector function with n component by f, be defined as follows:

$f\left({\hat{B}}_j\right)=\left(\begin{array}{c}0\\ f_1({\hat{B}}_j\left(1\right)-{\hat{B}}_j\left(2\right))\\ .\\ .\\ .\\ f_{m-2}({\hat{B}}_j(m-2)-{\hat{B}}_j(m-1))\\ f_{m-1}({\hat{B}}_j(m-1)-{\hat{B}}_j\left(m\right))\\ \left(0\right)\end{array}\right)-\left(\begin{array}{c}{f}_1({\hat{B}}_j\left(1\right)-{\hat{B}}_j\left(2\right))\\ f_2({\hat{B}}_j\left(2\right)-{\hat{B}}_j\left(3\right))\\ .\\ .\\ .\\ f_{m-1}({\hat{B}}_j(m-1)-{\hat{B}}_j\left(m\right))\\ 0\\ \left(0\right)\end{array}\right)$

Then, concrete differential equation (1.13) is considered:

Wherein λ >=0.

By interpolation, there are just real-valued or zero two positive functions and can introduce restriction condition like a cork in ordinal relation, thus provide:

$f\left({\hat{B}}_j\right)=\left(\begin{array}{c}{f}_0(B_j^{\min }-{\hat{B}}_j\left(1\right))\\ f_1({\hat{B}}_j\left(1\right)-{\hat{B}}_j\left(2\right))\\ .\\ .\\ .\\ f_{m-2}({\hat{B}}_j(m-2)-{\hat{B}}_j(m-1))\\ f_{m-1}({\hat{B}}_j(m-1)-{\hat{B}}_j\left(m\right))\\ \left(0\right)\end{array}\right)-\left(\begin{array}{c}{f}_1({\hat{B}}_j\left(1\right)-{\hat{B}}_j\left(2\right))\\ f_2({\hat{B}}_j\left(2\right)-{\hat{B}}_j\left(3\right))\\ .\\ .\\ .\\ f_{m-1}({\hat{B}}_j(m-1)-{\hat{B}}_j\left(m\right))\\ f_m({\hat{B}}_j\left(m\right)-B_j^{\max })\\ \left(0\right)\end{array}\right)$

If we only consider ordinal relation, this is equivalent to be described as:

$B_j^{\min }=-\&infin;\mathrm{et}{B}_j^{\max }=+\&infin;$

The convergence of this new estimating apparatus is set up due to following Lyapunov function:

● $\mathrm{\&Psi;}\left({\hat{B}}_j\right)=\frac{1}{2}({\hat{B}}_j-B_j)H^{-1}{({\hat{B}}_j-B_j)}^T$

●Ψ(B _j)＝0

● $\mathrm{\&Psi;}\left({\hat{B}}_j\right)>0,\mathrm{pour}{\hat{B}}_j\&NotEqual;B_j$

● $\frac{\mathrm{d\&Psi;}}{\mathrm{dt}}=-{\mathrm{\&beta;}}_j{({\hat{y}}_j-y_j)}^2+\mathrm{\&lambda;}({\hat{B}}_j-B_j)f{\left({\hat{B}}_j\right)}^T\&le;0$

The Section 2 of derivative can be expressed as followsin:

$({\hat{B}}_j-B_j)f{\left({\hat{B}}_j\right)}^T=\underset{i=1}{\overset{m-1}{\mathrm{\&Sigma;}}}((B_j\left(i\right)-B_j(i+1))+({\hat{B}}_j(i+1)-{\hat{B}}_j\left(i\right)))f_i({\hat{B}}_j\left(i\right)-{\hat{B}}_j(i+1))$

by following equation provide item and:

$(B_j\left(i\right)-B_j(i+1))f_i({\hat{B}}_j\left(i\right)-{\hat{B}}_j(i+1))+({\hat{B}}_j(i+1)-{\hat{B}}_j\left(i\right))f_i({\hat{B}}_j\left(i\right)-{\hat{B}}_j(i+1))$

By hypothesis, due to Bj (1)≤...≤Bj (m) and f _ifor just, so Section 1 is negative again.With Section 2 be negative or zero:

$({\hat{B}}_j(i+1)-{\hat{B}}_j\left(i\right))f_i({\hat{B}}_j\left(i\right)-{\hat{B}}_j(i+1))\&RightArrow;\left\{\begin{array}{cc}=0& \mathrm{si}{\hat{B}}_j(i+1)-{\hat{B}}_j\left(i\right)\&GreaterEqual;0\\ \&le;0& \mathrm{si}{\hat{B}}_j(i+1)-{\hat{B}}_j\left(i\right)\&le;0\end{array}\right.$

Therefore, the solution of differential equation restrains on the collection being feature with LaSalle principle of invariance.This collection is as follows:

$\left\{{\hat{B}}_j\right|\frac{\mathrm{d\&Psi;}}{\mathrm{dt}}=0\}=\{{\hat{B}}_j|{\hat{y}}_j=y_j\mathrm{et}{\hat{B}}_j\left(1\right)\&le;...\&le;{\hat{B}}_j\left(m\right)\}$

About the note of sub-example

Consider that the formula of restriction gives multiple degree of freedom: namely to limit, the value of function f and weight coefficient λ.Give the example of the selection of the function of sub-example 1.3.A as follows:

$f\left({\hat{B}}_j\right)=\max (0,B_{\min }-{\hat{B}}_j)+\min (0,B_{\max }-{\hat{B}}_j)$

With B in Fig. 8 _min=200 and B _max=400 charts again generating this function.

According to the form that function f adopts, weight coefficient lambda can be selected from following list:

The linear function of-form

$f\left({\hat{B}}_j\right)=\max (0,B_{\min }-{\hat{B}}_j)+\min (0,B_{\max }-{\hat{B}}_j)$ As shown in Figure 8.

●1/dt

● ${\mathrm{\&beta;}}_j\frac{H}{\max \left(H\right)}\frac{1}{\mathrm{dt}}$

● $\frac{H}{\max \left(H\right)}\frac{1}{\mathrm{dt}}$

-form logarithmic function

●1/dt

●2/dt

● ${\mathrm{\&beta;}}_j\frac{H}{\max \left(H\right)}\frac{1}{\mathrm{dt}}$

● $2{\mathrm{\&beta;}}_j\frac{H}{\max \left(H\right)}\frac{1}{\mathrm{dt}}$

In the application of refinery

Fig. 9 shows the estimation amount (in units of ppm) by performing the sulphur relevant with discrete time (correspond to and mix the recipe correction iterations after starting) that equation (1) obtains.

This application relate to the potpourri with three kinds of components fuel oil preparation, using regulate two kinds of quality and the fact that a kind of and wrong initial mass value in component is associated as special characteristic.

In the figure:

-curve C 1 shows the estimation of the sulfur content of the component 1 (wrong initial value) of potpourri;

-curve C 2 shows the estimation of the sulfur content of the component 2 of potpourri; And

-curve C 3 shows the estimation of the sulfur content of the component 3 of potpourri.

At this, find that the estimating apparatus of equation (1) completes the detection (excessively estimating) of improper value, it is corrected downwards, but this correction is inadequate and other is estimated the distribution of qualitative residual deviation and causes the negative estimation of sulfur content (its definition on must remain just or zero).

Figure 10 shows the estimation amount (in units of ppm) being corrected, realized, employ by equation (1.1) that adapt to rule, relevant with discrete time (the recipe correction iterations after corresponding to mixing) sulphur by δ, described δ is defined by equation as defined above (1.4), and by the part 1.4C of example 1.4 that is described in more accurately below.

At this, find that the estimating apparatus revised completes error recovery value (excessively estimating), and the quality keeping other to estimate just is.

Finally, find by add-ins δ, curve C 1 to C3 restrains.

example 1.4: have by the distribution corrected in delta (delta) characteristic estimated about the feedback of bundle condition

This example relates to the iso-prediction and calculation of vectorial δ, so that the special characteristic characteristic of contrast estimation.Or at each iteration system ground or the matrix of estimation characteristic in mode with good conditionsi, this vector being added into component.

sub-example 1.4.A: equality constraint manages

For correlation properties, (it has identical value (b for two kinds of base-materials ₁=b ₂)), solution based on:

$b_1=b_2\&DoubleLeftRightArrow;b_1-b_2=0\&DoubleLeftRightArrow;\left(\begin{array}{ccc}1& -1& \left(0\right)\end{array}\right)\left(\begin{array}{c}{b}_1\\ b_2\\ .\\ .\\ .\end{array}\right)=0$

For three kinds of base-materials, obtain following equation in an identical manner:

$b_1=b_2=b_3\&DoubleLeftRightArrow;\left\{\begin{array}{c}{b}_1-b_2=0\\ b_2-b_3=0\end{array}\right.\&DoubleLeftRightArrow;\left(\begin{array}{cccc}1& -1& 0& \left(0\right)\\ 0& 1& -1& \left(0\right)\end{array}\right)\left(\begin{array}{c}{b}_1\\ b_2\\ b_3\\ .\\ .\\ .\end{array}\right)=0$

By the matrix A formed by 0,1 and-1 _jbe integrated in constraint condition.Index j refers to characteristic j.Circulation is there is not, to avoid the redundancy in the source that numerical instability and order are lost in constraint matrix in a series of equation.Such as, this means, for the situation of above-mentioned three kinds of base-materials, there is no b ₃-b ₁the additional constraint condition of=0 type.

There is at most n-1 capable, n is the quantity of base-material.Therefore, new constraint condition is represented as follows:

Especially, because multiple estimations of differential equation (1.1) are different, the correction provided by δ makes it possible to keep equal in whole time course.Then, the problem revised is described to:

Lacking new lab analysis time, Δ is zero.Otherwise it equals diagonal angle weight matrix W can not necessarily insert in discriminant.

Because the first row is by being all that positive item forms, and other row only comprises a pair 1 and-1, so total constraint matrix it is non-singular matrix.Therefore, the linear applications joined with this matrix correlation is surjection, and it ensures the existence of at least one feasible point.In addition, because constraint condition forms convex set and discriminant is convex function, to separate and solution has uniqueness so exist.

This solution can be conclusivelyed show by introducing Lagrangian and applying optimal condition.Lagrangian is written as:

$L(\mathrm{\&delta;},\mathrm{\&lambda;},\mathrm{\&mu;})=\frac{1}{2}{\left|\right|(\mathrm{\&delta;}-\mathrm{\&Delta;})W\left|\right|}^2+\mathrm{\&lambda;\&delta;u}+{\mathrm{\&mu;}}^T{A}_j({\mathrm{\&delta;}}^T+{\hat{B}}_j^T)$

For this solution, its derivative is zero, and obtains the following explicit expression about δ:

sub-example 1.4.B: total ordinal relation management

Such as, for given characteristic, we consider the potpourri with the four kinds of base-materials sorted in the following order: b ₂≤ b ₃≤ b ₁≤ b ₄.This can be represented as:

$b_2\&le;b_3\&le;b_1\&le;b_4\&DoubleLeftRightArrow;\left\{\begin{array}{c}{b}_2-b_3\&le;0\\ b_3-b_1\&le;0\\ b_1-b_4\&le;0\end{array}\right.\&DoubleLeftRightArrow;\left(\begin{array}{cccc}0& 1& -1& 0\\ -1& 0& 1& 0\\ 1& 0& 0& -1\end{array}\right)\left(\begin{array}{c}{b}_1\\ b_2\\ b_3\\ b_4\end{array}\right)\&le;0$

Then, the problem that be solved is as follows:

Be different from the situation of equation, matrix A _jagain comprise n-1 capable and comprise all base-materials pair.The existence of feasible point comes from the result of equation situation.This is because know that existence makes δ.Convexity makes solution have uniqueness.But this problem does not have clear and definite solution and it needs to depend on convenient value optimization.

sub-example 1.4.C: limitation management

In order to keep becoming physical proportions with the estimation of the component characteristic in line computation, new constraint condition can be used.The interpolation of the restriction in estimated characteristic is carried out in the space that search can accept δ value.Then, this problem is:

To Farkas lemma be wandered back to for proving that the result relevant with the existence of the solution of proposed various problems is useful.

Farkas lemma:

One in following two characteristics and only one can be true:

There is the x meeting Ax≤b in ■, or

There is v >=0 and make vA=0 and vb < 0 in ■.

Use Farkas lemma, suppose it may be shown as the problems referred to above has solution all the time.

sub-example 1.4.D: the management of equality constraint and restriction

Thus, problem is:

Use Farkas lemma, suppose it may be shown as the problems referred to above has solution all the time.

sub-example 1.4.E: the management of restriction and total ordinal relation

Thus, problem is expressed as:

The matrix of constraint condition is no longer surjection.Therefore, not reentry the existence of at least one feasible point: one group of constraint condition may be infeasible.

Use Farkas lemma, suppose it may be shown as the problems referred to above has solution all the time.

sub-example 1.4.F: the management of restriction and part order relation

We consider n kind base-material altogether.The base-material quantity deferring to ordinal relation is called as m (< n), and supposes that they are m base-material originally and the order sequence increased gradually according to index.Replace even if it means, this is also possible all the time.These give following problem:

Use Farkas lemma, suppose it may be shown as the problems referred to above has solution all the time.

sub-example 1.4.G: distribution constraint condition

Express the general considerations of enable various types of distribution constraint condition (ordinal relation between the estimation of equation, restriction, component characteristic) as follows:

$\underset{\mathrm{\&delta;}}{\min }\frac{1}{2}{\left|\right|\mathrm{\&delta;}-\mathrm{\&Delta;}\left|\right|}^2$

Use Farkas lemma, suppose it may be shown as the problems referred to above has solution all the time.

For the space of 10 kinds of base-materials, provide the concrete instance of this sub-example at this.Formula and following matrix is given in table 1.1 initial value:

Table 1.1

Consider following relation:

$\left\{\begin{array}{c}\mathrm{lb}\&le;{\hat{B}}_1\&le;{\hat{B}}_3={\hat{B}}_4\&le;{\hat{B}}_8\&le;{\hat{B}}_9\&le;\mathrm{ub}\\ \mathrm{lb}\&le;{\hat{B}}_5={\hat{B}}_6={\hat{B}}_7\&le;\mathrm{ub}\\ \mathrm{lb}\&le;{\hat{B}}_2\&le;\mathrm{ub}\\ \mathrm{lb}\&le;{\hat{B}}_{10}\&le;\mathrm{ub}\end{array}\right.$

Limit as follows:

lb＝0 and ub＝90

Verified between two kinds of restrictions.

Solution is calculated according to least square solution function.Result is given in table 1.2:

Table 1.2

The estimation corrected consider the constraint condition applied.

sub-example 1.4.H: the management of stream row container

At this, be used to the characteristic estimated in the container of characteristic and the isolation estimated in district's separation panel container by the correction of vectorial δ.Be different from those characteristics in the continuous feed container easily developed in whole mixed process, the characteristic in the container of isolation does not change in whole mixed process (supposing to have suitable homogenizing).

Express this problem as follows:

$\underset{\mathrm{\&delta;}}{\min }\frac{1}{2}{\left|\right|\mathrm{\&delta;}-\mathrm{\&Delta;}\left|\right|}^2$

δu＝0

Wherein $\mathrm{\&Delta;}\left(i\right)={\stackrel{\&OverBar;}{B}}_j\left(i\right)-{\hat{B}}_j\left(i\right)=\left\{\begin{array}{c}0\\ B_0\left(i\right)-{\hat{B}}_j\left(i\right)\end{array}\right..$

Stream is made to arrange the container free time and attempt the estimation of the characteristic in other container to bring back in their lab analysis value.

sub-example 1.4.I: the special case with the component of mixing (minimized/maximized) target

The consideration of part order relation can be applied to minimize or component that trend to optimum target is associated in addition characteristic on be favourable.The part order of the estimation come into question can be considered according to the order defined by the initial mass value (usually being provided by lab analysis) of component at the beginning.

sub-example 1.4.J: the special case of high or low saturation degree estimation

Minimum and maximum restriction that is regular in adaptation and that may use in the calculating of updating vector δ is uncertain.For given characteristic, when all estimations are saturated in minimum or maximum restriction, suspect that it may be rational for having wrong limits value.Therefore, it is useful for there is the stage detecting these situations, so that tension and relaxation is subsequently noted the value of the restriction of wrong (incriminated).

detect

For maximum restriction, such as:

$\begin{array}{c}\&ForAll;i,\mathrm{active\; base},{\hat{B}}_j\left(i\right)=B_j^{\max }\\ \&DoubleDownArrow;\\ \underset{\mathrm{active\; base}}{\mathrm{\&Sigma;}}{\hat{B}}_j\left(i\right)u_i=B_j^{\max }\underset{\mathrm{active\; base}}{\mathrm{\&Sigma;}}{u}_i=B_j^{\max }\end{array}$

At this, can suppose that the actual value of characteristic is greater than by observing also this situation can be detected.Similarly, pass through the minimum limit of mistake detected.

tension and relaxation

If saturation degree should be detected in estimation, then required tension and relaxation restriction.The restriction that a kind of middle definition in the following two kinds mode is new:

Table 1.3

example 1.5: the feedback with the average control value on decentralized measure

When each computing interval does not refresh decentralized measure, following equation (its history using the comprehensive past to control is average) can be used to determine the matrix corrected

The solution of this equation restrains and meets

Introduce as minor function:

$\mathrm{\&Psi;}\left({\hat{B}}_j\right)=\frac{1}{2}({\hat{B}}_j-B_j)H^{-1}{({\hat{B}}_j-B_j)}^T$

This function meets following characteristic:

●Ψ(B _j)＝0

● for ${\hat{B}}_j\&NotEqual;B_j,$ $\mathrm{\&Psi;}\left({\hat{B}}_j\right)>0$

Its derivative equals:

$\underset{\&OverBar;}{\frac{\mathrm{d\&Psi;}}{\mathrm{dt}}=-\frac{B_j}{\mathrm{\&delta;t}}({\hat{B}}_j-B_j)\underset{t-\mathrm{\&delta;t}}{\overset{t}{\&Integral;}}u({\hat{B}}_{j}u-y_j^{\mathrm{mes}})\mathrm{dt}}$

Provide the selection of gap length, do not have new estimation to be calculated in the time interval [t-δ t, t].Then, following equation can be write out:

$\underset{\&OverBar;}{\frac{\mathrm{d\&Psi;}}{\mathrm{dt}}=-\frac{B_j}{\mathrm{\&delta;t}}\underset{t-\mathrm{\&delta;t}}{\overset{t}{\&Integral;}}{({\hat{B}}_{j}u-y_j^{\mathrm{mes}})}^2\mathrm{dt}}$

The time-derivative of function Ψ is negative.Therefore, the function introduced for this system is obviously Lyapunov function.Therefore, this solution towards the convergence of Lasalle collection, thus proves determined result.

When decentralized measure, only new measurement available instead of each iteration system to calculate new estimation may be favourable.In addition, to the order near the moment obtaining and measure sample, to be averaged be possible.This average computation makes the impact of any inaccuracy in transfer delay be limited.Propose following realization:

Wherein Δ is the transfer delay be associated with characteristic j.

parameter arranges and realizes

Must select the length of moving window, this must depend on delay.Dat recorder error based on about 20% and propose following parameter arrange:

$\mathrm{\&delta;t}=\frac{\mathrm{\&Delta;}}{5}.$

example 2.1: the feedback with premixed, the control in momentary mode

This example class is similar to example 1.1, but corresponds to specific base-material and to mix with other base-material with situation about being pre-mixed before forming the potpourri expected at them.

Fig. 2 shows the example of the topology of 6 kinds of base-material mixing.

Consider the equipment of p the compounding operation comprised represented by 1 to p.Make:

-Q _it () is the volume flow rate of base-material i at moment t, i ∈ 1 ... n};

-Q _n+it () is in the total volume flow rate of dead volume of moment t by being associated with compounding operation i, i ∈ 1 ... p} (input flow velocity always equals to export flow velocity);

-Q (t) is in the total volume flow rate of moment t by mixer,

-V _iit is the dead volume be associated with compounding operation i; And

-b _ithe eigen vector of base-material i, (with respectively) be eigen vector when moment t enters (and exiting respectively) compounding operation j.Usually, for base-material b _i:

Make path ∏ _ibe associated with each base-material i, described path is by a series of p _idead volume defines, and this base-material passes through described dead volume to arrive mixer.This path is a series of different integer p _i, it is relevant to the numeral index of compounding operation, for any j ∈ 1 ..., p _ihave p _i=0, mean in the direct injecting mixer of base-material i.

When Fig. 2, we have:

∏ ₁＝{3}，p ₁＝1，

∏ ₂＝{2，3}，p ₂＝2

∏ ₃＝{2；3}，p ₃＝2

p ₄＝0

∏ ₅＝{1}，p ₅＝1

∏ ₆＝{1}，p ₆＝1。

For any compounding operation i, we define its q _ithe set r of individual input flow velocity _i.This is the q relevant to the index for volume flow rate of encoding _ithe set of individual different integer, r _i= for any j ∈ 1 ..., q _ihave

When Fig. 2, we have:

r ₁＝{5，6}，q ₁＝2

r ₂＝{2，3}，q ₂＝2

r ₃＝{1，6+3}＝{1，9}，q ₃＝2。

For characteristic b _ibe included in weighting (weighted) the form Q of the expression formula for admixture characteristic _i(t)/Q (t) b _iin, described potpourri adopts the form of the linear combination of base-material characteristic.

Now, let us is back to situation.

For compounding operation overall flow rate is input characteristics provided by following formula:

$b_{{\mathrm{\&pi;}}_i^1}^E\left(t\right)=\frac{{\mathrm{\&Sigma;}}_{j\&Element;{\mathrm{\&Gamma;}}_{{\mathrm{\&pi;}}_i^1}}{b}_j^E{Q}_j\left(t\right)}{{\mathrm{\&Sigma;}}_{j\&Element;{\mathrm{\&Gamma;}}_{{\mathrm{\&pi;}}_i^1}}{Q}_j\left(t\right)}.$

In this input, b _iin item occur with following form:

$\frac{Q_i\left(t\right)}{{\mathrm{\&Sigma;}}_{j\&Element;{\mathrm{\&Gamma;}}_{{\mathrm{\&pi;}}_i^1}}{Q}_j\left(t\right)}{b}_i=\frac{Q_i\left(t\right)}{Q_{{\mathrm{\&pi;}}_i^1}\left(t\right)}{b}_i$

As output, we have pure delay defined by following equation:

$V_{{\mathrm{\&pi;}}_i^1}={\&Integral;}_{t-{\mathrm{\&delta;}}_{{\mathrm{\&pi;}}_i^1}\left(t\right)}^t{Q}_{{\mathrm{\&pi;}}_i^1}\left(\mathrm{\&tau;}\right)\mathrm{d\&tau;}.---\left(3\right)$

Therefore, b _iin item exist with following form middle appearance:

$\frac{Q_i(t-{\mathrm{\&delta;}}_{{\mathrm{\&pi;}}_i^1}\left(t\right))}{Q_{{\mathrm{\&pi;}}_i^1}(t-{\mathrm{\&delta;}}_{{\mathrm{\&pi;}}_i^1}\left(t\right))}{b}_i.$

Similarly, for compounding operation we have:

$b_{{\mathrm{\&pi;}}_i^2}^E\left(t\right)=\frac{{\mathrm{\&Sigma;}}_{j\&Element;{\mathrm{\&Gamma;}}_{{\mathrm{\&pi;}}_i^2}}{b}_j^E{Q}_j\left(t\right)}{{\mathrm{\&Sigma;}}_{j\&Element;{\mathrm{\&Gamma;}}_{{\mathrm{\&pi;}}_i^2}}{Q}_j\left(t\right)},$

That is, for middle b _iitem

$\frac{Q_{{\mathrm{\&pi;}}_i^1}\left(t\right)}{Q_{{\mathrm{\&pi;}}_i^2}\left(t\right)}\frac{Q_i(t-{\mathrm{\&delta;}}_{{\mathrm{\&pi;}}_i^1}\left(t\right))}{Q_{{\mathrm{\&pi;}}_i^1}(t-{\mathrm{\&delta;}}_{{\mathrm{\&pi;}}_i^1}\left(t\right))}{b}_{i.}$

For b _iin item occur with following form:

$\frac{Q_{{\mathrm{\&pi;}}_i^1}(t-{\mathrm{\&delta;}}_{{\mathrm{\&pi;}}_i^2}\left(t\right))}{Q_{{\mathrm{\&pi;}}_i^2}(t-{\mathrm{\&delta;}}_{{\mathrm{\&pi;}}_i^2}\left(t\right))}\frac{Q_i(t-{\mathrm{\&delta;}}_{{\mathrm{\&pi;}}_i^2}\left(t\right)-{\mathrm{\&delta;}}_{{\mathrm{\&pi;}}_i^1}(t-{\mathrm{\&delta;}}_{{\mathrm{\&pi;}}_i^2}\left(t\right)))}{Q_{{\mathrm{\&pi;}}_i^1}(t-{\mathrm{\&delta;}}_{{\mathrm{\&pi;}}_i^2}\left(t\right)-{\mathrm{\&delta;}}_{{\mathrm{\&pi;}}_i^1}(t-{\mathrm{\&delta;}}_{{\mathrm{\&pi;}}_i^2}\left(t\right)))}{b}_i.$

We see at path ∏ _ithe composition of the delay of middle appearance.Let us defined function: for ∏ _iin any be defined as follows at the composition of these functions at fixing j place:

And

${\mathrm{\&Delta;}}_i^{l,k,j}\left(t\right)\stackrel{\mathrm{\&Delta;}}{=}{\mathrm{\&Delta;}}_i^l\left({\mathrm{\&Delta;}}_i^{k,j}\left(t\right)\right).$

According to these definition, middle b _ithe formula of item provides as follows:

$\frac{Q_{{\mathrm{\&pi;}}_i^1}\left({\mathrm{\&Delta;}}_i^2\left(t\right)\right)}{Q_{{\mathrm{\&pi;}}_i^2}\left({\mathrm{\&Delta;}}_i^2\left(t\right)\right)}\frac{Q_i\left({\mathrm{\&Delta;}}_i^{\mathrm{1,2}}\left(t\right)\right)}{Q_{{\mathrm{\&pi;}}_i^1}\left({\mathrm{\&Delta;}}_i^{\mathrm{1,2}}\left(t\right)\right)}{b}_i.$

Leaving last compounding operation time, for b _iin we have:

$\frac{Q_{{\mathrm{\&pi;}}_i^{p_i-1}}\left({\mathrm{\&Delta;}}_i^{p_i}\left(t\right)\right)}{Q_{{\mathrm{\&pi;}}_i^{p_i}}\left({\mathrm{\&Delta;}}_i^{p_i}\left(t\right)\right)}\frac{Q_{{\mathrm{\&pi;}}_i^{p_i-2}}\left({\mathrm{\&Delta;}}_i^{p_i-1,p_i}\left(t\right)\right)}{Q_{{\mathrm{\&pi;}}_i^{p_i-1}}\left({\mathrm{\&Delta;}}_i^{p_i-1,p_i}\left(t\right)\right)}...\frac{Q_{{\mathrm{\&pi;}}_i^1}\left({\mathrm{\&Delta;}}_i^{2,...,p_i}\left(t\right)\right)}{Q_{{\mathrm{\&pi;}}_i^2}\left({\mathrm{\&Delta;}}_i^{2,...,p_i}\left(t\right)\right)}\frac{Q_i\left({\mathrm{\&Delta;}}_i^{\mathrm{1,2},...,p_i}\left(t\right)\right)}{Q_{{\mathrm{\&pi;}}_i^1}\left({\mathrm{\&Delta;}}_i^{\mathrm{1,2},...,p_i}\left(t\right)\right)}$

Further, finally, in the mixture, b _icoefficient entry passes through U _it () represents:

$U_i\left(t\right)=\frac{Q_{{\mathrm{\&pi;}}_i^{p_i}}\left(t\right)}{Q\left(t\right)}\frac{Q_{{\mathrm{\&pi;}}_i^{p_i-1}}\left({\mathrm{\&Delta;}}_i^{p_i}\left(t\right)\right)}{Q_{{\mathrm{\&pi;}}_i^{p_i}}\left({\mathrm{\&Delta;}}_i^{p_i}\left(t\right)\right)}\frac{Q_{{\mathrm{\&pi;}}_i^{p_i-2}}\left({\mathrm{\&Delta;}}_i^{p_i-1,p_i}\left(t\right)\right)}{Q_{{\mathrm{\&pi;}}_i^{p_i-1}}\left({\mathrm{\&Delta;}}_i^{p_i-1,p_i}\left(t\right)\right)}...\frac{Q_{{\mathrm{\&pi;}}_i^1}\left({\mathrm{\&Delta;}}_i^{2,...,p_i}\left(t\right)\right)}{Q_{{\mathrm{\&pi;}}_i^2}\left({\mathrm{\&Delta;}}_i^{2,...,p_i}\left(t\right)\right)}\frac{Q_i\left({\mathrm{\&Delta;}}_i^{\mathrm{1,2},...,p_i}\left(t\right)\right)}{Q_{{\mathrm{\&pi;}}_i^1}\left({\mathrm{\&Delta;}}_i^{\mathrm{1,2},...,p_i}\left(t\right)\right)}.---\left(4\right)$

Therefore, for u _i(t)=u _i(t)=Q _i(t)/Q (t), and output is expressed as:

$y\left(t\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{U}_i\left(t\right)b_i---\left(5\right)$

Thus, for the situation of premixed, the equation (1) of dynamic system becomes:

$\frac{d{\hat{B}}_j^t}{\mathrm{dt}}=-{\mathrm{\&beta;}}_j\mathrm{HU}\left(t\right)(y_j\left(t\right)-y_j^{\mathrm{mes}}\left(t\right)),---\left(2\right)$

U (t)=(U ₁(t) ..., U _n(t)) ^t, U _it () value is by equation (4) definition and by equation (5) definition y (t)=(y ₁(t) ..., y _m(t)) ^t.

The function used when not having premixed remains the Lyapunov function of this new dynamic system and demonstrates restrain to BU.

example 2.2: the feedback with premixed: normalization and the example realized

This example class is similar to example 2.1, but corresponding to having the normalization of topology of multiple premixeds and the concrete general solution of realization of mixer upstream.

By being used for, symbol dV represents that the premixed be associated with premixed volume V postpones.

A. many premixeds topological matrix

At this, the matrix describing general topology is used to define the dead volume be associated with maximum vector, and described maximum vector comprises the n kind base-material of the maximal sequence of k the premixed level as possibility sequence, knows following situation, for giving deciding grade and level, parallel multiple compounding operation can be defined.

The maximum dimension (n kind base-material and k level) of topological matrix is the revisable parameter of configuration.

Every a line of matrix corresponds to given component base-material.

Each row of this matrix comprise the description of premixed level, have by produce in prime premixed, dead volume that the component base-material of premixed that coming into question with participation is associated or is associated with the grouping of premix base.

At this, the example of a practical topology comprises 3 premixed levels as described below:

Table 1.4: many premixeds topological matrix

Base-material	Level 1	Level 2	Level 3	Container
					1	V1	V1’	V1”	B1
2	V1	V1’	V1”	B2
					3	0	0
4	0	0	V2”	B4
					5	0	0	V2”	B5
6	V2	V1’	V1”	B6
					7	V2	V1’	V1”	B7
8	0	0	0
					9	0	0	0
10	0	0	V1”	B10
					11	0	0	0

This matrix describing many premixeds topology is used to the compounding operation, the base-material come into question and the dead volume be associated that identify serial (in multiple different level) and parallel (the premixed level given).

This formula has compact, complete, clear and general advantage.

According to current formulation (for switching to complementary tank etc. situation, according to this kind of or this container), formula of considering automatically is revised the premixed topology considered.

Above provided matrix example is the illustration of the topology shown in Figure 11.

The first order comprises two that be associated with dead volume V1 and V2, parallel compounding operation.

The second level comprises the single compounding operation be associated with dead volume V '.

The third level comprise respectively with dead volume V1 " and V2 " be associated, parallel two compounding operation.

Therefore, this topological matrix is read from left to right.

For given row (given component i) and for give deciding grade and level (row k):

If all elements (left-hand part of row) of index < k is zero in-row i, the base-material so come into question does not participate in any premixed of prime;

If an element (left-hand part of row) of index < k is non-zero in-row i, the base-material so come into question participates in the premixed of prime, and it then associates with premixed Late phase, described premixed postpones to be associated with the dead volume of the nonzero value corresponding to the element come into question.

In the case, the one group of component base-material be associated with identical dead volume must be back to, for the level come into question (in the row come into question in matrix): this component subset belonging to identical compounding operation enters one group of premix base in the level that coming into question.

Unique restriction of this matrix description is as follows: for this description, and it can not have the different premixed of that be associated from identical dead volume product value, parallel (in same stages) two.In the case, the base-material in each participating in two compounding operation is had no idea to distinguish: they are grouped in same compounding operation jointly.

B. single premixed

1., under the prerequisite of not premixed, the linear volume-based model used after the index conversion of component characteristic gives the value of following admixture characteristic j:

$y_j\left(t\right)=\underset{l}{\mathrm{\&Sigma;}}\mathrm{bi}*\mathrm{ui}\left(t\right)$

This equation makes it possible to mass matrix (the row vector component bi for characteristic j) according to B component and control vector U (component ui, it depends on time t) calculates mixing quality y _jprediction.

2. for single compounding operation, this equation becomes (postponing dV for premixed) the following general formula represented by [2.2B2]:

$y\left(t\right)=\underset{i\&Element;\mathrm{PM}}{\mathrm{\&Sigma;}}\mathrm{bi}*\mathrm{ui}(t-\mathrm{dV})*\left(\underset{j\&Element;\mathrm{PM}}{\mathrm{\&Sigma;}}\mathrm{uj}\left(t\right)\right)/\left(\underset{j\&Element;\mathrm{PM}}{\mathrm{\&Sigma;}}\mathrm{uj}(t-\mathrm{dV})\right)+\underset{i\&NotElement;\mathrm{PM}}{\mathrm{\&Sigma;}}\mathrm{biui}\left(t\right)$

PM is the subset of the index of the component belonging to compounding operation.

The component not belonging to compounding operation is directly mixed to mixer.

Let us considers the following example with the base-material 1 and 2 of premixed and the base-material 3 and 4 of non-premixed, and its topology has been shown in Figure 12.

Overall flow rate F (t) leaving mixer is the portion flow rate sum of the upstream passageway Fi (t) corresponding with ratio ui (t).

The component i of compounding operation and ratio u ' i (corresponding to the portion flow rate of the pre-mixing passages divided by the overall flow rate of pre-mixing passages, in this case Fl (t)) is associated.

This overall flow rate of pre-mixing passages is relevant to the premixed product being feature with characteristic value yl (t).

Mixer exports product with characteristic value y for feature.

Input component i has characteristic value qi and dV is the delay of compounding operation.

The quality y (t) of product at moment t is provided by following equation:

y(t)＝(F1(t)/F(t))y1(t)+q3＊u3+q4＊u4

Also there is following equation: y1 (t)=u ' 1 (t-d) q1+u ' 2 (t-dV) q2.

In addition, F1 (t)=(u1 (t)+u2 (t)) F (t) and u ' i (t) F1 (t)=ui (t) F (t), i=1 or 2.

Therefore, u ' i (t-dV)=ui (t-dV)/(u1 (t-dV)+u2 (t-dV)).

Finally,

y(t)＝q1＊u1(t-dV)(u1(t)+u2(t))/(u1(t-dV)+u2(t-dV))

+q2＊u2(t-dV)(u1(t)+u2(t))/(u1(t-dV)+u2(t-dV))

+q3＊u3+q4＊u4

This is the expression corresponding with the general formula of single compounding operation [2.2B2].

C. parallel many compounding operation

For multiple compounding operation parallel in single level, above equation becomes:

$y\left(t\right)={\mathrm{\&Sigma;}}_{k\&Element;\mathrm{PM}\left(e\right)}(\underset{i\&Element;\mathrm{PM}(e,k)}{\mathrm{\&Sigma;}}\mathrm{bi}*\mathrm{ui}(t-\mathrm{dV}(k,e))*\left(\underset{j\&Element;\mathrm{PM}(e,k)}{\mathrm{\&Sigma;}}\mathrm{uj}\left(t\right)\right)/\left(\underset{j\&Element;\mathrm{PM}(e,k)}{\mathrm{\&Sigma;}}\mathrm{uj}(t-\mathrm{dV}(k,e))\right)+\underset{i\&NotElement;\mathrm{PM}(e,k)}{\mathrm{\&Sigma;}}\mathrm{biui}\left(t\right))+{\mathrm{\&Sigma;}}_{i\&NotElement;\mathrm{PM}(e,k\&ForAll;\mathrm{kPM}\left(e\right))}\mathrm{biui}\left(t\right)$

Suppose that given base-material not to participate in same rank parallel two different compounding operation: therefore, have relevant to the base-material of premixed for various continuous print compounding operation and list.

PM (e) is a group index k of the parallel compounding operation of the level e come into question.

PM (e, k) be the base-material of the compounding operation k belonged to as prime e a group index k ' (by with in i or j represent).

DV=dV (k, e) is the delay of the current compounding operation k of the level e come into question.

D. serial and parallel multiple compounding operation

For serial and parallel multiple compounding operation, the program adopted is progression step by step, using the beginning base-material be associated with the current control vector do not postponed as beginning, the output computing relay of every one-level control vector and this vector is sent to next stage.

The control vector of the delay of the output of afterbody will be by the control vector of the delay of the control operation be used in synchronizing characteristics estimation equation.

For the example that we describe in table 1.4, the base-material do not participated in any pre-premixed of the first order is base-material 3,4,5,8,9 and 10.

The effect of these base-materials is as follows:

$\underset{i\&NotElement;\mathrm{PM}\left(k\right)\&ForAll;k\&Element;\mathrm{PM}\left(1\right)}{\mathrm{\&Sigma;}}\mathrm{biui}\left(t\right)=b3u3\left(t\right)+b4u4\left(t\right)+b5u5\left(t\right)+b8u8\left(t\right)+b9u9\left(t\right)+b10u10\left(t\right)$

The base-material participating in compounding operation premixV1 is: u1 and u2.

The base-material participating in compounding operation premixV2 is: u6 and u7.

The effect of these base-materials is as follows:

$\underset{i\&Element;\mathrm{premixV}1}{\mathrm{\&Sigma;}}\mathrm{bi}*\mathrm{ui}(t-\mathrm{dV}1)*\left(\underset{j\&Element;\mathrm{premixV}1}{\mathrm{\&Sigma;}}\mathrm{uj}\left(t\right)\right)/\left(\underset{j\&Element;\mathrm{premixV}1}{\mathrm{\&Sigma;}}\mathrm{uj}(t-\mathrm{dV}1)\right)+$

$\underset{i\&Element;\mathrm{premixV}2}{\mathrm{\&Sigma;}}\mathrm{bi}*\mathrm{ui}(t-\mathrm{dV}2)*\left(\underset{j\&Element;\mathrm{premixV}2}{\mathrm{\&Sigma;}}\mathrm{uj}\left(t\right)\right)/\left(\underset{j\&Element;\mathrm{premixV}2}{\mathrm{\&Sigma;}}\mathrm{uj}(t-\mathrm{dV}2)\right)+$

For this first order, premixed postpones δ V1 and δ V2 and is associated with dead volume V1 and V2 of two compounding operation will considered respectively on base-material 1,2 and base-material 6,7 respectively.

Expect that control vector VR (t) of the delay calculated will have following form:

$y_j\left(t\right)=\underset{i}{\mathrm{\&Sigma;}}\mathrm{bi}*\mathrm{VRi}\left(t\right)$

Then, the control vector of the delay of the output of level 1 will be expressed in the following manner:

The control vector of this delay of level 1 is represented by VR1.

The component be associated with the base-material not participating in any compounding operation of this vector will be the respective component not having vicissitudinous current control vector: VR1i (t)=ui (t).

In contradistinction to, the synchronous process will be subject to as Types Below with the component that the base-material really participated in the compounding operation " premix " that has and postpone dV is associated of this vector:

$\mathrm{VR}1i\left(t\right)=\mathrm{ui}(t-\mathrm{dV})*\left(\underset{j\&Element;\mathrm{premix}}{\mathrm{\&Sigma;}}\mathrm{uj}\left(t\right)\right)/\underset{j\&Element;\mathrm{premix}}{\mathrm{\&Sigma;}}\mathrm{uj}(t-\mathrm{dV}))$

The calculating of VR1 uses current control vector u (t).

Therefore, for the example in table 1.4, VR1 will be defined by following component:

1 u1(t-dV1)＊[U1+U2(t)]/[U1+U2(t-dV1)]

2 u2(t-dV1)＊[U1+U2(t)]/[U1+U2(t-dV1)]

3 u3(t)

4 u4(t)

5 u5(t)

6 u6(t-dV2)＊[U6+U7(t)]/[U6+U7(t-dV2)]

7 u7(t-dV2)＊[U6+U7(t)]/[U6+U7(t-dV2)]

8 u8(t)

9 u9(t)

10 u10(t)

For the control vector (representing to have component VR1i=VR1 (i) by VR1) being used in the delay of the output of prime in level input is used as current control by the control vector (being represented by VR2) of the delay of level 2 calculating.

This second level is defined by the compounding operation be associated with the dead volume V1 ' and phase delay dV1 ' of base-material 1,2,6 and 7.

Therefore, VR2 will be defined by following component:

1 VR11(t-dV1’)＊VR11+VR12(t)+VR16+VR17(t)]/[VR11+VR12+VR16+VR17(t-dV1’)]

2 VR12(t-dV1’)＊[VR11+VR12(t)+VR16+VR17(t)]/[VR11+VR12+VR16+VR17(t-dV1’)]

3 VR13(t)

4 VR14(t)

5 VR15(t)

6 VR16(t-dV1)＊[VR11+VR12(t)+VR16+VR17(t)]/[VR11+VR12+VR16+VR17(t-dV1’)]

7 VR17(t-dV1’)＊[VR11+VR12(t)+VR16+VR17(t)]/[VR11+VR12+VR16+VR17(t-dV1’)]

8 VR18(t)

9 VR19(t)

10 VR110(t)

For the control vector (representing to have component VR2i=VR2 (i) by VR2) being used in the delay of prime output in level input is used as current control by the control vector (being represented by VR3) of the delay of level 3 calculating.

On the one hand by having the dead volume V1 with base-material 1,2,6,7 and 10 " the delay dV1 that is associated " compounding operation and on the other hand by having the dead volume V2 with base-material 4,5 " the delay dV2 that is associated " the second compounding operation define this third level.

Therefore, VR3 will be defined by following component:

1 VR21(t-dV1”)＊[VR21+VR22+VR26+VR27+VR210(t)]/

[VR21+VR22+VR26+VR27+VR210(t-dV1”)]

2 VR22(t-dV1”)＊[VR21+VR22+VR26+VR27+VR210(t)]/

[VR21+VR22+VR26+VR27+VR210(t-dV1”)]

3 VR23(t)

4 VR24(t-dV2”)＊[VR24+VR25(t)]/[VR24+VR25(t-dV2”)]

5 VR25(t-dV2”)＊[VR24+VR25(t)]/[VR24+VR25(t-dV2”)]

6 VR26(t-dV1”)＊[VR21+VR22+VR26+VR27+VR210(t)]/

[VR21+VR22+VR26+VR27+VR210(t-dV1”)]

7 VR27(t-dV1，，)＊[VR21+VR22+VR26+VR27+VR210(t)]/

[VR21+VR22+VR26+VR27+VR210(t-dV1”)]

8 VR28(t)

9 VR29(t)

10 VR210(t-dV1”)＊[VR21+VR22+VR26+VR27+VR210(t)]/

[VR21+VR22+VR26+VR27+VR210(t-dV1”)]

For these three grades of topologys, the vector of the last delay then used in the application rule of the matrix B of component will be the output of level 3 calculate that, namely VR3 as defined above.

The General Recursive formulism of the control E. postponed

In the output of level k, obtain form VR according to following content _k=f (VR _k-1) the recurrence formula of control vector of delay:

VR _k, the vector of the delay of the output of level k;

VR _k-1, the vector of the delay of the output of level k-1.

Therefore, will by following equation definition VR _k:

$\left[\begin{array}{c}{\mathrm{VR}}_{(k-1)}i(t-\mathrm{dV}(k,p_k))*\\ \left(\underset{j\&Element;\mathrm{PM}(k,p_k)}{\mathrm{\&Sigma;}}{\mathrm{VR}}_{(k-1)}j\left(t\right)\right)/\underset{j\&Element;\mathrm{PM}(k,p_k)}{\mathrm{\&Sigma;}}{\mathrm{VR}}_{(k-1)}j(t-\mathrm{dV}(k,p_k)))\\ \mathrm{ifi}\&Element;\mathrm{PM}(k,p_k)\\ {\mathrm{VR}}_{(k-1)}i\left(t\right)\\ \mathrm{ifi}\&NotElement;\mathrm{PM}(k,p_k)\&ForAll;p_k\&Element;\mathrm{Pk}\end{array}\right]$

Above, dV (k, p _k) be (in Pk the compounding operation of level k) compounding operation p _kpremixed postpone, consider add up to K level for the topology that will be processed.

PM (k, p _k) be the compounding operation p of grade k _kthe subset of base-material.

F. the implicit use of variable delay

According to the compounding operation p with level k _kthe dead volume be associated and according to flow relocity calculation variable delay: dV (k, p _k).

For variable delay management, the implicit formula of the controlling value (instead of delay) being obtained the delay be associated with the given dead volume in level by interpolation advantageously can be used at this.

Recursive list for the control of the delay of the cascade of serial/parallel compounding operation reaches the combination meaning delay that this variable delay is the topology considering to define, that be associated with the dead volume of the various compounding operation of " front " level.

G. equivalent topologies

If this compounding operation moves to level 1 (V3) or level 2 (V2 '), the compounding operation V2 according to level 3 place " topoligical equivalence that proposes at this:

Table 1.5: there is V2 " matrix:

Base-material	Level 1	Level 2	Level 3	Container
					1	V1	V1’	V1”	B1
2	V1	V1’	V1”	B2
					3	0	0
4	0	0	V2”	B3
					5	0	0	V2”	B4
6	V2	V1’	V1”	B5
					7	V2	V1’	V1”	B6
8	0	0	0
					9	0	0	0
10	0	0	V1”	B7
					11	0	0	0

The equivalent matrix of V3 (=V2 "):

Practical topology comprises three premixed levels:

Table 1.6

Base-material	Level 1	Level 2	Level 3	Container
					1	V1	V1’	V1”	B1
2	V1	V1’	V1”	B2
					3	0	0
4	V3	0	0	B4
					5	V3	0	0	B5
6	V2	V1’	V1”	B6
					7	V2	V1’	V1”	B7
8	0	0	0
					9	0	0	0
10	0	0	V1”	B10
					11	0	0	0

The equivalent matrix of V2 ' (=V3=V2 "):

Practical topology comprises three premixed levels:

Table 1.7

Base-material	Level 1	Level 2	Level 3	Container
					1	V1	V1’	V1”	B1
2	V1	V1’	V1”	B2
					3	0	0
4	0	V2’	0	B4
					5	0	V2’	0	B5
6	V2	V1’	V1”	B6
					7	V2	V1’	V1”	B7
8	0	0	0
					9	0	0	0
10	0	0	V1”	B10
					11	0	0	0

example 3: majorizing sequence

Control method according to the present invention uses optimizer to determine the u that fills a prescription in sub-step (3) period of step (ii).This optimizer comprises above-mentioned steps (a) to (d).Optimizer is realized and this optimizer transmits the formula u that optimized to estimating apparatus 13 to determine to be applied to the formula of the control device 10 of equipment by optimizer 14.

Below, describe with reference to Fig. 3 and be used for the example of operation of optimizer of optimization of C/C composites u.

Symbol:

We consider M={1,2 ..., the following subset of m}, is assigned to the set of the index of output:

● R, exports the subset of index, and the setting value in the benchmark calculated in aggregative model or momentary mode is specified for the subset of described output index;

● H _m, export the subset of index, be called as the minimum limit that " firmly " limits, be that is specified for the subset of described output index as the restriction that preferentially must be taken seriously;

● H _m, export the subset of index, hard maximum restriction is specified for the subset of described output index;

● S _m, export the subset of index, be called as the minimum limit that " soft " limits, that is do not have the restriction of priority to be specified for the subset of described output index; And

● S _m, export the subset of index, soft maximum restriction is specified for the subset of described output index.

Contemplated what can be associated with each output is at most benchmark (or setting value), minimum (hard or soft) limits and maximum (hard or soft) limits.Therefore inherently, and

In addition, assuming that consider the impact of estimated adjuvant in the value of benchmark and constraint condition.

About benchmark the equation that must be considered is:

$y=y_i^{\mathrm{ref}},\&ForAll;i\&Element;R.$

be by the corresponding row of the index only retained with belong to R from the matrix of middle extraction.By introducing vectorial y _rwith this inequality set is rewritten as this is the constraint condition on unknown u.

Constraint condition set in output provides as follows:

$\left\{\begin{array}{cc}{y}_i\&GreaterEqual;y_i^{\min }& \&ForAll;i\&Element;H_m\\ y_i\&le;y_i^{\max }& \&ForAll;i\&Element;H_M\\ y_i\&GreaterEqual;y_i^{\min }& \&ForAll;i\&Element;S_m\\ y_i\&le;y_i^{\max }& \&ForAll;i\&Element;S_M\end{array}\right.$

by only retaining and belonging to H _mthe relevant row of index and from the matrix of middle extraction.By introducing vector with first set of inequality is rewritten as this is the constraint condition on unknown u.By simileys,

$\left\{\begin{array}{c}{\hat{B}}_{H_m}u\&GreaterEqual;y_{H_m}^{\min }\\ {\hat{B}}_{H_M}u\&le;y_{H_M}^{\max }\\ {\hat{B}}_{S_m}u\&GreaterEqual;y_{S_m}^{\min }\\ {\hat{B}}_{S_M}u\&le;y_{S_M}^{\max }\end{array}\right.$

Certainly, this inequality set is equivalent to

$\left\{\begin{array}{c}-{\hat{B}}_{H_m}u\&le;{-y}_{H_m}^{\min }\\ {\hat{B}}_{H_M}u\&le;y_{H_M}^{\max }\\ -{\hat{B}}_{S_m}u\&le;-y_{S_m}^{\min }\\ {\hat{B}}_{S_M}u\&le;y_{S_M}^{\max }\end{array}\right.$

Make:

$\begin{array}{cccc}{B}_H=\left(\begin{array}{c}-B_{H_m}\\ B_{H_M}\end{array}\right)& B_S=\left(\begin{array}{c}-B_{S_m}\\ B_{S_M}\end{array}\right)& y_H^{\max }=\left(\begin{array}{c}-y_{H_m}^{\min }\\ y_{H_M}^{\max }\end{array}\right)& y_S^{\max }=\left(\begin{array}{c}-y_{S_m}^{\min }\\ y_{S_M}^{\max }\end{array}\right)\end{array}.$

Inequality set finally provides as follows:

$\left\{\begin{array}{c}{\hat{B}}_{H}u\&le;y_H^{\max }\\ {\hat{B}}_{S}u\&le;y_S^{\max }\end{array}\right.$

Therefore, according to above-mentioned symbol, symbol for exporting any set P of the index be associated with these.For the single output of index j, symbol is only

Initial optimization problem P0 (whole issue) is to find out closest to benchmark formula while still meeting the constraint condition set on u formula u.This problem not necessarily has solution.If it does not have solution, it still must generate new formula, and according to the present invention, this new formula is separated multiple continuous print optimization problem by order and obtains:

-first (problem P1), by from limit priority hard constraint condition to the iterative processing of lowest priority hard constraint condition, search the acceptable value for the hard constraint condition exported;

-secondly (problem P2), search the acceptable value for benchmark; And

-last (problem P3), by from limit priority soft-constraint condition to the iterative processing of lowest priority soft-constraint condition, searches the acceptable value for the soft-constraint condition exported.

Table 1 describes the example of majorizing sequence.

Table 1: majorizing sequence P0 to P3

Relevant with the value of ratio as the minimum/maximum of the base-material of permanent precedence constraints, know by using total output flow velocity of mixer with m ³/ h represents hydraulic pressure minimum/maximum.

Rate of change (ROC) is approximately 25% usually.

In order to prepare the potpourri of gasoline types, the number percent of hard minimum value normally density, octane value and extraction, and hard maximal value normally sulfur content, density, vapour pressure, volatility, benzene content, olefin(e) centent and arene content.And be contrary for soft minimum value and maximal value, except density, it has its minimum value as hard-threshold and maximum threshold.

In order to prepare the potpourri of hydrocarbon type, soft minimum value is sulfur content, density, filtrability and cloud point normally, and the number percent of soft maximal value normally flash-point, cetane rating and extraction.And be contrary for hard minimum value and maximal value.

In order to prepare the potpourri of fuel type, hard minimum value normally viscosity and hard maximal value normally viscosity, sulfur content and density.

Explain the various continuous problems that may use below in detail.

Initial problem P0

Initial problem P0 is used in the execution of the step (a) of above-mentioned optimizer.The solution of this whole adjustment problem P0 comprises the optimization of C/C composites u considering the constraint condition on component ratio and the constraint condition on admixture characteristic.

This problem is the constraint condition set that the formula that meets is upper and export, and the benchmark on exporting, and simultaneously from the angle of least square, is the minimum potential range of distance benchmark formula.

Thus, be by the problem of separating:

$\underset{u}{\min }{\left|\right|u-\stackrel{\&OverBar;}{u}\left|\right|}^2$

$\left\{\begin{array}{c}{u}^{\min }\&le;u\&le;u^{\max }\\ {\mathrm{\&Sigma;}}_{i=1}^n{u}_i=1\\ {\hat{B}}_{R}u=y_R^{\mathrm{ref}}\\ {\hat{B}}_{H}u\&le;y_H^{\max }\\ {\hat{B}}_{S}u\&le;y_S^{\max }\end{array}\right.$

In the optimization problem that this is formulated, as optimized variable, be expect the vectorial u of calculated formula.

Replacement scheme is to propose similar optimization problem, and described similar optimization problem has, as optimized variable, for the bias vector e of the deviation between initial baseline formula and the formula u of component ratio.

When this problem has solution u ^*time, it is employed.If not this situation, then separate three following problem P1 to P3 continuously.

For this problem P0, the constraint condition that be satisfied is:

(1) constraint condition on binder ratio:

Zero hydraulic restriction condition (inequality): each passage i may transmit with between flow velocity.For current flow F, for each base-material, it is required:

$u_i^{p,\min }=\frac{F_i^{\min }}{F}\&le;u_i\&le;u_i^{p,\max }=\frac{F_i^{\max }}{F}$

Zero scheduling constraint (inequality): they correspond to the minimum and maximum incorporation (its ratio summation equals 1) of each base-material.For momentary mode, it causes least commitment condition and maximum constraint

Zero incorporation change constraint condition (inequality): the ratio of each base-material i can not with more than ratio change downwards and with more than ratio upwards change.Thus, if be u in the ratio of front charging _i, the current command must be greater than and be less than

Zero constant total output flow velocity equality constraint (summation of binder ratio must equal 1);

(2) constraint condition on admixture characteristic:

The zero inequality constrain condition be associated with adjustment equation, described adjustment equation represents that measured value y must meet its setting value y _sp(by introducing tolerance limit (tolerance) if be formulated-do not have these tolerance limits with the form of inequality constrain condition, the formulism of equality constraint type may be needed);

Zero keeps the inequality constrain condition of characteristic value in min/max scope measured, thus meets specification and limit excessive setting.

In this problem, the standard expected can be expressed as the deviation relevant to the initial formulation expecting to be minimized, and still ensures to have met whole above-mentioned constraint condition simultaneously.

When problem P0 intangibility (considering that the mixing of all required specifications is infeasible), start the majorizing sequence of three step P1, P2 and P3.

Problem P1: the management of hard constraint condition

Executive problem P1 in the step (b) of above-mentioned optimizer.

Thus, determine that minimal adjustment problem P1 is by the formula u separated, its P0 that only considers a problem is defined as the constraint condition of precedence constraints.This problem P1 comprises a succession of normally feasible optimization problem, and its standard is the punishment to violating described precedence constraints, thus for the accessible new value of these precedence constraints definition.

These standards correspond to the precedence constraints by hierarchical arrangement of the inequality type in monitored characteristic, preferably, the hard constraint condition by hierarchical arrangement according to regulate target and do not meet the relevant priority arrangement of increase (incurring) cost that the specifications of quality comprises.

This problem P1 relates to iterative manner management hard constraint condition (constraint condition on binder ratio and the precedence constraints on admixture characteristic) by reducing priority.Because multiple constraint condition may have equal priority, complete iteration management by the constraint condition set of equal priority is incompatible.

What be associated with each constraint condition is grade.By convention, the lower grade be associated with constraint condition, and the priority of constraint condition is lower.Positive grade is associated with precedence constraints, and negative grade is associated with non-preferential constraint condition.

Consider to divide H=H _m∪ H _mfor p whole nonvoid subset H _i, each subset set index corresponding with the object output of the hard constraint condition of equal priority.By building, p≤card (H), and H _i∩ H _j=Φ, as long as i < is j, with H _jrelevant constraint condition have than with H _ithe priority that those relevant constraint conditions are lower.Should also be noted that

iteration 1: with H ₁the process of the limit priority constraint condition be associated.

Following problem must be separated:

$\underset{u,\mathrm{\&zeta;}}{\min }{\left|\right|{\hat{B}}_{H_1}u+\mathrm{\&zeta;}-y_{H_1}^{\max }\left|\right|}^2$

$\left\{\begin{array}{c}{u}^{\min }\&le;u\&le;u^{\max }\\ \mathrm{\&zeta;}\&GreaterEqual;0\\ {\mathrm{\&Sigma;}}_{i=1}^n{u}_i=1\end{array}\right.$

Wherein ζ is deviation variable vector (or lax vector), and described ζ makes it possible to the dimension of increase superior vector (u, ζ) and calculates the optimum error corresponding with the tension and relaxation of constraint condition.

When the initial value of u meets the equality constraint in restriction and its element summation, this problem has solution, and it is this situation always.

Time suitable, separate (u ^*, ζ ^*) allow optimization problem by tension and relaxation.

By the card (H of ζ ₁) element ζ _jiteration, can value be reached be defined as foloows:

If-ζ _j> 0, so can reach the initial value that value is constraint condition;

If-ζ _j=0, so can reach value is

iteration k+1:

When (k+1) secondary iteration, separate following problem:

$\underset{u,\mathrm{\&zeta;}}{\min }{\left|\right|{\hat{B}}_{H_{k+1}}u+\mathrm{\&zeta;}-y_{H_{k+1}}^{\max }\left|\right|}^2$

$\left\{\begin{array}{c}{u}^{\min }\&le;u\&le;u^{\max }\\ \mathrm{\&zeta;}\&GreaterEqual;0\\ {\mathrm{\&Sigma;}}_{i=1}^n{u}_i=1\\ {\hat{B}}_{H_{1k}}u\&le;y_{H_{1k}}^{\max ,\mathrm{att}}\end{array}\right.$

Because for set H ₁to H _krelevant constraint condition defines and can reach value at k, so this problem always has solution in front iteration.

Be similar in front iteration, time suitable, separate (u ^*, ζ ^*) make it possible to tension and relaxation optimization problem.By the card (H of ζ _k+1) element ζ _jiteration, as follows definition can reach value

If-ζ _j> 0, so can reach the initial value that value is constraint condition; And

If-ζ _j=0, so can reach value is

When separating p sub-portfolio (subassembly) of the constraint condition that priority reduces during P iteration, this problem is separated completely.

Thus, by Filled function, sequence P1 is used for separating hard constraint condition (the positive ordering constraint condition on the constraint condition on binder ratio and admixture characteristic).In infeasible situation, the constraint condition of lowest priority is by tension and relaxation.When its can not meet required whole time, use sequence.Hard constraint condition has higher weight compared with fixing set point adjustment target.The soft-constraint condition of negative grade is out in the cold.Still formulation optimization is not carried out in this sequence.

Problem P2: the management of benchmark

Problem P2 is comprised in step (c) period of above-mentioned optimizer.

Thus, determine that adjustment problem P2 is by the described non-preferential constraint condition reaching new value and problem P0 of the precedence constraints of the formula u separated, its P0 that considers a problem.This problem P2 comprises optimization problem, and its standard is the punishment to violating described non-preferential constraint condition, thus for the accessible new value of these non-preferential constraint condition definition.

These standards correspond to the equality constraint in priority that fixing setting value regulates, preferably, and non-preferential soft grade (soft-rank) constraint condition relevant to regulating target, but cause excessive quality.

This sequence comprises hard constraint set of circumstances, and having its value may by the restriction of tension and relaxation during sequence P1.Problem P2 seeks to meet adjustment formula as much as possible, even if it needs tension and relaxation setting value for reaching setting value in due course.These formula are all handled simultaneously (this sequence P2 is not iteration).

But introduce weighing vector by the associated weight character of the importance associated of operating characteristic in standard, the orientation of tension and relaxation is possible, thus the preferentially the most unessential characteristic of tension and relaxation.

The soft-constraint condition of negative grade is out in the cold and still do not carry out the optimization of filling a prescription.

To be by the problem of separating:

$\underset{u}{\min }{\left|\right|{\hat{B}}_{R}u-y_R^{\mathrm{ref}}\left|\right|}^2$

$\left\{\begin{array}{c}{u}^{\min }\&le;u\&le;u^{\max }\\ {\mathrm{\&Sigma;}}_{i=1}^n{u}_i=1\\ {\hat{B}}_{H}u\&le;y_H^{\max ,\mathrm{att}}\end{array}\right.$

Because the whole hard constraint condition of tension and relaxation during the solution of problem P1, so this problem always has solution u ^*.Benchmark can be reached be calculated as

Problem P3: the management of soft-constraint condition

Problem P3 is comprised in step (d) period of above-mentioned optimizer.

Determine that adjustment problem P3 is by the formula u separated, its described new reached value considering the precedence constraints of the problem P0 obtained in step (b), described new the reached value of non-preferential constraint condition obtained in step (c) and not by other non-preferential constraint conditions all of the problem P0 of problem P1 and P2 process.This problem P3 comprises a succession of normally feasible optimization problem, and its standard is the punishment to violating other non-preferential constraint condition described, thus for the accessible new value of these other non-preferential constraint condition definition.

These standards correspond to the non-preferential constraint condition by hierarchical arrangement of the inequality type in monitored characteristic.

This problem relates to management soft-constraint condition iteratively.This comprises the sequence management of the constraint condition bag reduced by priority.According to the mode being similar to problem P1, introduce S=S _m∪ S _msubset S _i.

iteration 1: with S ₁the process of the limit priority constraint condition be associated.

Following problem must be separated:

$\underset{u,\mathrm{\&zeta;}}{\min }{\left|\right|{\hat{B}}_{S_1}u+\mathrm{\&zeta;}-y_{S_1}^{\max }\left|\right|}^2$

$\left\{\begin{array}{c}{u}^{\min }\&le;u\&le;u^{\max }\\ \mathrm{\&zeta;}\&GreaterEqual;0\\ {\mathrm{\&Sigma;}}_{i=1}^n{u}_i=1\\ {\hat{B}}_{H}u\&le;y_H^{\max ,\mathrm{att}}\\ {\hat{B}}_{R}u=y_R^{\mathrm{Ref},\mathrm{att}}\end{array}\right.$

Time suitable, separate (u ^*, ζ ^*) make it possible to tension and relaxation optimization problem.By the card (S of ζ ₁) element ζ _jiteration, can value be reached be defined as foloows:

If-ζ _j> 0, so can reach the initial value that value is constraint condition;

If-ζ _j=0, so can reach value is

iteration k+1:

When (k+1) secondary iteration, separate following problem:

$\underset{u,\mathrm{\&zeta;}}{\min }{\left|\right|{\hat{B}}_{S_{k+1}}u+\mathrm{\&zeta;}-y_{S_{k+1}}^{\max }\left|\right|}^2$

$\left\{\begin{array}{c}{u}^{\min }\&le;u\&le;u^{\max }\\ \mathrm{\&zeta;}\&GreaterEqual;0\\ {\mathrm{\&Sigma;}}_{i=1}^n{u}_i=1\\ {\hat{B}}_{H}u\&le;y_H^{\max ,\mathrm{att}}\\ {\hat{B}}_{R}u=y_R^{\mathrm{Ref},\mathrm{att}}\\ {\hat{B}}_{S_{1k}}u\&le;y_{S_{1k}}^{\max ,\mathrm{att}}\end{array}\right.$

Be similar in front iteration, time suitable, separate (u ^*, ζ ^*) make it possible to tension and relaxation optimization problem.By the card (S of ζ _k+1) element ζ _jiteration, as follows definition can reach value

If-ζ _j> 0, so can reach the initial value that value is constraint condition;

If-ζ _j=0, so can reach value is

When the subset of the constraint condition of all solutions priority reduction, this problem is separated completely.

If possible, this sequence P3 makes it possible to consider soft-constraint condition, this depends on their grade, and meet (not necessarily by tension and relaxation) adjustment formula simultaneously, described adjustment formula have on constraint condition on binder ratio and admixture characteristic not necessarily by the hard constraint condition of tension and relaxation.

Process the constraint condition of same levels in majorizing sequence simultaneously.Still formulation optimization is not carried out.

Whole the solving of optimization problem completes after the last iteration of problem P3, its part u separated ^*it is the calculated order that will be applied to mixer.

Preferably, for each problem, ensure the constraint condition do not violated on binder ratio and the constraint condition do not violated in binder ratio summation, described summation must equal 1.Therefore, consider these constraint conditions always.

Fig. 3 shows the sequence of optimization problem P0 to P3 defined above.

If the numerical solution of initial problem P0 does not provide solution, then the order of starting problem P1, P2 and P3 solves.Although these problems always have solution in theory, their numerical solution may failure.The formula following (see Fig. 3) of method is applied to according to solving failure:

Situation 1: the formula of application is the result of initial optimization problem;

Situation 2: the formula of application is actual formula;

Situation 3: the formula of application is the result calculating P1;

Situation 4: the formula of application is the result calculating P2; And

Situation 5: the formula of application is the result calculating P3.

When the numerical solution failure of problem P1 to P3 and when continuing tension and relaxation hard constraint condition when separating problem P1, activation output monitoring.This monitoring is to check following content:

-with setting value y ^c _ithe output y be associated _istill exist with between scope in, wherein t ^cit is user-defined tolerance limit; And

-only with minimum limit y ^minand/or maximum restriction y ^maxthe output be associated does not have exceedance y ^min-t ^minand/or y ^max+ t ^max, wherein t ^minand t ^maxit is user-defined threshold value.

If exceed threshold value, then stop the order being used for potpourri.

It should be noted that and use and initial formulation u ⁰relevant deviation e instead of directly carry out code optimization problem according to variable u.

Otherwise characteristic estimating apparatus self uses and encodes according to u instead of according to the coding of deviation e, thus exempt the use of initial mixing-initiation measurement, it is usually inaccurate.

In addition, according to the coding according to variable u of the present invention and above-mentioned completely compatible according to feedback process of the present invention.

Will be noted that the possible different order of magnitude by the middle characteristic that considers a problem, the demarcation (scaling) of the formula comprised in the optimization problem proposed considers that (gets round) numerical value regulates the problem of (numerical conditioning).

This demarcation is to use the multiplication scale-up factor (scale factor) in right side and the left side being applied to various constraint condition.

This coefficient adjusts according to the characteristic in problem:

By using, as normalized value, the average of the extreme value (minimum and maximal value) of constituent mass performs this proving operation (when characteristic is not associated with setting value).

Equally, as normalized value is average (when characteristic is associated with setting value) between the average of constituent mass extreme value (minimum and maximal value) and possible setting value.

And normalization is also applied in optimizing criterion P1, P2, P3.

The norm used corresponds to the quadratic form that diagonal matrix defines, and its diagonal term is the inverse square of calculated scale-up factor.

Example 4: the optimization in aggregative model

a. the constraint condition on admixture characteristic

When control model is momentary mode, the constraint condition that user defines on admixture characteristic is those constraint conditions for optimizing, and particularly, target is the setting value that user directly provides.

In Comprehensive Control pattern, user may consider the constraint condition management in the calculated cumulative volume characteristic having flowed into container in cumulative volume characteristic in container and container-aggregative model when not being on instantaneous admixture characteristic but from the mixing in potpourri-aggregative model.This leaves tolerance (latitude) in the definition of the instantaneous constraint condition for optimizing.

Obviously, the value defined for the constraint condition be associated with the cumulative volume flowed into by user can be adopted, but as explained in detail, these constraint conditions can by tension and relaxation below.

If pass through z ^krepresent the current composite value of admixture characteristic and pass through z ^k+1represent integrated value during (k+1) secondary iteration, for current volume V ^k, current flow F ^kto pass T in period (or being used as multiple periods of flow range (sliding horizon)), be positioned at the currency y of the characteristic of mixer output ^kmake it possible to connect z ^kto z ^k+1, thus:

V ^kz ^k+F ^kTy ^k＝(V ^k+F ^kT)z ^k+1。

If the constraint condition that user provides is z ^max(similar in described process and least commitment condition), in current iteration, following formula must be applied:

$y^k\&le;\frac{(V^k+F^{k}T)z^{\max }-V^k{z}^k}{F^{k}T}$

The right side of this inequality provides y ^kmaximum restriction, its may with z ^maxcomplete difference, but can be used for by selecting y ^max=z ^maxand avoid excessively limiting transient command.On the contrary, as itself and z ^maxthis restriction is undesirably applied: be greater than z time very not identical ^maxthe y of+t ^maxtension and relaxation be not allowed to, z ^maxbe the constraint condition applied of user and t is tolerance limit defined by the user equally.

b. the management of benchmark

In momentary mode, the characteristic regulated is the characteristic in mixer outlet.In the case, the benchmark used during optimizing equals user-defined setting value.

In container-bottom-aggregative model, the characteristic regulated is the characteristic in the storage container of potpourri inflow.User-defined setting value is relevant to the characteristic in container.For optimization, Calculation Basis from these setting values.

Some characteristics in momentary mode and other characteristic in aggregative model can also be regulated.

-potpourri storage container is empty situation (or " potpourri "-aggregative model, to distinguish over " container-aggregative model ") when mixing and starting.

Symbol:

● y _j(t), the characteristic j at mixer outlet place is in the value of moment t;

● z _j(t), the value of the overall characteristic j of the volume of inflow, corresponds to the overall characteristic j of potpourri at moment t at this;

● V (t), the volume flowed into time from mixing, corresponds to the volume of potpourri at moment t at this; And

● F (t), in the total volume flow rate of moment t by mixer.

Pass through simple mass balance:

$\frac{\mathrm{dV}\left(t\right)}{\mathrm{dt}}=F\left(t\right)$ And $\frac{d\left(V\left(t\right)z_j\left(t\right)\right)}{\mathrm{dt}}=F\left(t\right)y_j\left(t\right).$

For moment t ₀and t ₁, wherein t ₁>=t ₀if, y _jwith F at t ₀and t ₁between be constant, so:

V (t ₁)=V (t ₀)+F (t ₀) (t ₁-t ₀), and

F(t ₀)(t ₁-t ₀) y _j(t ₀)+V(t ₀) z _j(t _o)＝(V(t _o)+F(t ₀)(t ₁-t ₀)) z _j(t ₁)。

Definition datum means the constant value that the characteristic calculating mixer outlet place must adopt thus at the end of the time H (flow range that user selects) from current time t, overall characteristic z _jfrom its currency z _jt () becomes setting value

Thus, following formula is applied:

$F\left(t\right){\mathrm{Hy}}_j^{\mathrm{ref}}+V\left(t\right)z_j\left(t\right)=(V\left(t\right)+F\left(t\right)H)z_j^c$

Namely,

$y_j^{\mathrm{ref}}=z_j^c+\frac{V\left(t\right)}{F\left(t\right)H}(z_j^c-z_j\left(t\right)).$

In each iteration, upgrade benchmark based on this formula (flow range).

-potpourri storage container is not empty situation when mixing and starting.

The calculating in path must be revised.

If initial volume is V ₀and the initial value of characteristic j is z in container _j0, so:

$F\left(t\right)H{y}_j^{\mathrm{ref}}+V\left(t\right)z_j\left(t\right)+V_O{z}_{\mathrm{jo}}=(V_O+V\left(t\right)+F\left(t\right)H)z_j^c$

Wherein V (t) is the volume flowed into from mixing, corresponds to the volume of potpourri at moment t at this.

In order to avoid the saltus step in benchmark, preferably, progressively instead of single ground consider the volume of container bottom.

For this reason, defining virtual setting value thus:

$z_j^{\mathrm{cv}}=z_j^c+a\frac{V_0}{V\left(t\right)+F\left(t\right)H}(z_j^c-z_{j0})$

When a equals 0, there is not container bottom.

When a equals 1, consider whole container bottom.Therefore, it enough completes the change of 0 to 1 to consider container bottom step by step along predetermined particular path.

example 5: the management of adjuvant

The adjuvant (alloy) of a small amount of injection plays a part essence and strong to potpourri characteristic.When there is not the constraint condition in additive flow rate, the characteristic be doped may be almost completely neglected in optimization-sequence multivariable Control problem.Then, single argument regulator additive flow rate acted on is used to regulate this characteristic.Such as, this is the adjuvant injecting controller 18 of the said equipment.The operation of this regulator is described below.

It should be noted that following preliminary explanation:

Effect in the-characteristic that affected by the injection of alloy is considered to instantaneous.But for any characteristic, there is transfer delay, it may depend on the value of measurement.In a practical situation, by hypothesis, transfer delay and measured value may connect by it;

-quantize the impact of alloy on characteristic poorly.Its change is relevant to the currency of the characteristic be doped.Even if some each value that is inaccurate and that adopt for the characteristic be doped, by hypothesis, the change of the change of alloy flow velocity with the value being doped characteristic may connect by it.

The model used is expressed as:

$\frac{\mathrm{dy}}{\mathrm{dt}}=K\left(y\right)\frac{\mathrm{dv}}{\mathrm{dt}},$

Wherein

● y is the measured value being doped characteristic

● v is alloy flow velocity; And

● k is the gain depending on the currency being doped characteristic.Hypothesis existed the piece-wise constant function being used for the y describing this gain.

From discrete viewpoint, when iteration k:

Δy ^k＝K(y ^k)Δv ^k

Be y to allow currency ^koutput trend towards its reference value y ^ref.r, Δ v ^k=(y ^ref.r-y ^k)/K (y ^k) be sufficient.But because transfer delay, available output is not currency in the value of k.Therefore, this program must based on calculating the estimated value exported on order and by following formulae discovery order:

${\mathrm{\&Delta;v}}^k=(y^{\mathrm{ref}.r}-{\hat{y}}^k)/K\left({\hat{y}}^k\right).$

Estimated value two sums:

-open loop estimated value (it uses ),

The deviation of-filtering drawn from the first-order filtering of transient deviation, synchronous with the deviation between measured value and open-loop prediction value.

Transfer delay δ T corresponds to each measured value y ^k, wherein T is the nutrition of this order.By this delay of piece-wise constant function representation of hypothesis y.Thus, measured value y ^kcorresponding to open-loop prediction value make it possible to calculate transient deviation according to transfer delay Lookup protocol filter factor.

For order, management following constraint:

-be changed to the maximum change of senior or rudimentary injection;

-minimum and maximum injection.

In instantaneous value regulates, it can not input the setting value outside the extreme value of user's setting.

In integrated value regulates, reference path (its may comprise consider the bottom of container) calculates according to those the similar modes used with multivariate order.Particularly, the instantaneous benchmark calculated according to setting value can not depart from the extreme value that user is arranged.In practice, this allows to meet and the characteristic that regulates arranges constraint condition.

When alloy flow velocity is saturated (when order still equals the minimum of predetermined instant or maximal value), it may switch to via base-material the adjustment being doped characteristic.

In the case, the value adopted before the flow velocity that adulterates still equals to switch.

For the output be doped, at the moment t that mixing starts ₀with the accumulative effect that the alloy between moment t causes provides as follows:

That is, from the angle of discrete:

When switching to the adjustment of characteristic j via base-material, control model is considered this effect and is provided as follows:

This expression formula is used for Filled function and feedback system dynamic system in.

Example 6: the optimization of formula

When degree of freedom is still in the Xie Zhongshi of the formula used in optimization, it can optimize the preparation of potpourri by amendment formula, that is respective ratio of each base-material.For the majorizing sequence described in example 3, the various options of optimization of C/C composites will be described in this example.

In the initial optimization problem P0 described in example 3, it is for minimizing item problem.

This benchmark formula in this expression formula value depend on the Optimizing Mode that user selects.

(a) lack optimization

equal initial value simply, that is user is the beginning of mixing and the formula that provides.

" following (follower) " formula can also be defined as, so its value equals the mean value of the u from mixing.

(b) the optimization of specific base-material incorporation

It may maximize or minimize the incorporation of specific base-material, exceedes and generates on-the-spot available amount or almost do not have on the contrary.In the case, priority vector π must be associated with formula.

This vector comprises for the positive input of the base-material that will be maximized and the negative input for the base-material that will be minimized.The base-material undesirably maximizing or minimize incorporation has 0 priority.

Thus, π=(π ₁..., π _n) ^tand | π _j|=max _{i=1, n}| π _i|, be assumed to be non-zero.

Pass through u ^frepresent the filter value of u, we use π ' ^fthe filter value of following amounts:

π′＝(π ₁/|π _j|，...，π _n/|π _j|) ^t。

This π filtering allows the formula change progressively considered between mixing period.

(c) the optimization of potpourri cost

Cost vector ξ=(ξ ₁..., ξ _n) ^tbe associated with u.For each by (pass), based on filtering formula u ^f: c=ξ ^fu ^fthe cost of definition formula.

Next, (c: non-zero) vectorial ξ ' is defined as follows:

ξ′＝((1-ξ ₁/C)，...，(1-ξ _n/C)) ^t。

Thus, if the cost that the cost of base-material is filled a prescription lower than current filtering, then ξ is passed through _i'=(1-ξ _i/ C)) ξ ' that defines _ifor just: in the case, needing to manage to mix this base-material limit the cost of filling a prescription.Otherwise, if the cost of base-material is greater than the cost of formula, then ξ _ibe negative.

For optimization,

(d) specification in output saturated

In the case, δ equals initial formulation, but in fact it only has a little importance.If this is because initial problem P0 has solution, so start iterative problem described below.

Make M={1,2 ..., m} is that the indexed set being assigned to output merges and makes P be the subset of indices indicating the output comprised in optimizer.

Be associated with each element j of P:

The element of-H, in other words:

The maximal value be not exceeded,

Or the minimum value be not lower than;

-threshold value the d relevant to constraint condition _j.

Consider that dividing P is p all nonvoid subset P _i, each subset gathers the index of the output optimizing demand corresponding to equal priority.By building, and

With P _jrelevant optimization and and P _ithose relevant optimizations are compared has more low priority, as long as i < is j.Notice equally

iteration 1

In first time iteration, object is to make to correspond to P ₁output close to their constraint condition:

$\underset{u}{\min }{\left|\right|{\hat{B}}_{P_1}u-y_{P_1}^{\max }+d_{P_1}\left|\right|}^2$

$\left\{\begin{array}{c}{u}^{\min }\&le;u\&le;u^{\max }\\ {\mathrm{\&Sigma;}}_{i=1}^n{u}_i=1\\ {\hat{B}}_{R}u=y_R^{\mathrm{ref}}\\ {\hat{B}}_{H}u\&le;y_H^{\max }\\ {\hat{B}}_{S}u\&le;y_S^{\max }\end{array}\right.$

Separate u ^*be used for calculating

iteration k+1

When (k+1) secondary iteration, separate following point:

$\underset{u}{\min }{\left|\right|{\hat{B}}_{P_{k+1}}u-y_{P_{k+1}}^{\max }+d_{P_{k+1}}\left|\right|}^2$

$\left\{\begin{array}{c}{u}^{\min }\&le;u\&le;u^{\max }\\ {\mathrm{\&Sigma;}}_{i=1}^n{u}_i=1\\ {\hat{B}}_{R}u=y_R^{\mathrm{ref}}\\ {\hat{B}}_{H}u\&le;y_H^{\max }\\ {\hat{B}}_{S}u\&le;y_S^{\max }\\ {\hat{B}}_{P_{1k}}u\&GreaterEqual;y_{P_{1k}}^{\min }\end{array}\right.$

When separating p sub-portfolio of the constraint condition that priority reduces during p iteration, this problem is separated completely.So, export as far as possible close to their constraint condition.

Example 7: continously hydrogen adding desulfurization mixer controls

Example 7 shows the adjustment of the instantaneous sulfur content value for the potpourri prepared by multiple base-material.

At this, can notice in multivariable Control situation, complete the monitoring of adjustment and other characteristic of potpourri in the adjustment of this sulphur and region concurrently.

This example has set forth the following ability of equipment: ensure that continuous instantaneous controls, and to have an effect on composition gas and oil hydrodesulphurization unit being loaded to (charge), thus controls the characteristic of the potpourri that this unit exports.

It also illustrates the ability that equipment control has the COMPLEX MIXED device upstream scheme of multiple component compounding operation.

Consider following factors:

-analyser postpone: when density, sulfur content (estimating apparatus resets on corresponding analysis instrument) and calculate extraction number percent be 5 minutes; Be 10 minutes when flash-point; And be 15 minutes when cloud point;

-shipped (transit) dead volume: 96m ³;

-premixed dead volume: be 16.8m in the first premixed level ³and 10.9m ³; Be 4.5m in the second premixed level ³; And be 10.8m in the 3rd premixed level ³and 1.4m ³.

Loading component is as follows:

Base-material 1: kerosene;

Base-material 2: the kerosene of low sulfur content;

Base-material 3: there is low and high-sulphur light diesel fuel, come from atmospheric distillation;

Base-material 4: from the moderate gas and oil of normal pressure and vacuum distillation;

Base-material 5: from the FCC LLCO alkene base-material of intermediate receptacle; And

Base-material 6:FCC heavy naphtha.

Other base-material can be used in loading this unit: FCC LLCO, HLCO and HCCS directly flow, VGO direct viscosity breaking gas and oil stream (direct unit stream), recycling from unit.

The character of the base-material 1 to 5 measured in the lab is provided in table 2 below:

Table 2: the character of the base-material of example 7

Except flash-point and cetane rating, be soft-threshold for individual minimum threshold.

Except cetane rating, flash-point and extraction number percent, be hard-threshold for individual max-thresholds.

Value for these minimum and maximum threshold values of various characteristic is as follows:

Table 3: the value of the minimum and maximum threshold value of the admixture characteristic of example 7

The reference path scope (reference path horizon) used is defined as the twice that analyser postpones, and is increased by the parameterisable value being called as reduction scope.The reduction scope used is as follows: be 10 minutes when density, cetane rating, sulfur content and extraction number percent; It is 20 minutes for flash-point; And be 30 minutes for cloud point.

Adjustment estimating apparatus filtration coefficient used is as follows: be 15 minutes for density, cetane rating, extraction number percent and sulfur content; It is 30 minutes for flash-point; And be 45 minutes for cloud point.These filtration coefficients (β occurred in formula defined above (1) and (2) _iinverse) correspond to the component parameter of vectorial β used in the differential equation of estimating apparatus, make it possible to idiocratically control relatively fast speed of convergence one by one.

Formulation optimization target is also used for maximizing base-material 1 (kerosene) and the use of base-material 4 (moderate distillation gas and oil).

Mix start time, the minimum and maximal value of sulfur content is 30 and 48ppm respectively.Then, amendment threshold value, becomes 2 and 8ppm respectively.Sulphur " in region " in its minimum and maximum restriction regulates.From [30,48] threshold value is to [2,8] this conversion of threshold value allows the switching from 50ppm step (be have sulfur content close to 48ppm to have the preparation limit of 2ppm in this object) to 10ppm step (be have the sulfur content close to 8ppm in this object, thus have the preparation limit of 2 i.e. m).

Table 4 specifies potpourri topology.

Table 4: the topology of the potpourri of example 7

Fig. 4 show sulfur content in potpourri from 50ppm step to during the rapid translating of 10ppm step to by the relevant change of number, each by corresponding to 5 minutes.That each once new execution (and the once new iteration therefore corresponded to according to control method of the present invention) by corresponding to according to equipment of the present invention and especially corresponding to is calculated by equipment and be applied to the transmission of the new formula of instrument.

In fact, provide setting value change by revising minimum and max-thresholds, the sulphur adjustment being informed in this is in region, that is performs between its minimum value and its maximal value.Therefore, this sulfur content quality does not have the target of fixing setting value-type, but its be at this optimised device consider and the qualitative high extreme value of this sulfur content of the target zone changed for this quality definition and low extreme value constraint condition.

To notice that the sulfur content of potpourri all keeps close to expectation value at any time, and follow setting value reduction order rapidly, and in value, there is no large unexpected change.

Estimating apparatus according to the present invention makes it possible to the adjustment of the sulfur content not only ensureing to leave unit but also regulates (flash-point is in least commitment condition, and sulfur content and cloud point are in maximum constraint) in the region of guarantee density, flash-point, cloud point, cetane rating and extraction number percent.

Fig. 5 shows the change in the consumption of the base-material 2 to 4 used during the amendment of sulfur content order, and in order to prepare potpourri, base-material 1,5 and 6 is not injected into.The characteristic that the component ratio calculated distribution shown in figure makes it possible to about leaving unit obtains the result expected.

Example 8: the gasoline mixture (not having premixed) in container-bottom-aggregative model

Fig. 6 a-e shows the binder ratio (adjustment (be respectively Fig. 6 b and 6c) of Fig. 6 a), on RON (research octane number (RON)) and RVP (Reid vapour pressure) and monitoring is over time in the region of the extraction number percent (Fig. 6 d) of 100 DEG C and benzene content (Fig. 6 e).

Container-integrated value, instantaneous value and setting value have been shown in Fig. 6 a to 6c.

For various component base-material, give to benzene content, in the extraction number percents of 100 DEG C, MON (motor octane number), value that RON (research octane number (RON)) and RVP (Reid vapour pressure) is relevant in the following table:

Table 5: the characteristic value of the base-material of example 8

This exemplifications set has the operation of the adjustment that container-bottom compensates.Two quality, i.e. vapour pressure and octane value, convergence, and other two quality, namely at extraction number percent and the benzene content of 100 DEG C, remain in their permissible scope.

To regulate and the minimum and maximal value of quality monitored provides with [min/max] form and as follows:

Benzene content (%): [0/0.95];

Extraction number percent (%) at 100 DEG C: [47/70];

RON:[95.199/96.50], there is minimum value 95.199 as setting value; And

RVP (mbar): [459.99/599.86], has the setting value of 598.86.

Can see, in the latter half of mixing by near 70, activity on base-material increases, because reached its low (minimum) extreme value in the quality of the extraction number percent of 100 DEG C, formula is automatically modified to improve its value and keeps this value on its minimum threshold, still keeps other institute to regulate being in the characteristic monitored their desired value simultaneously.

This example has set forth the following ability of equipment: be in their min/max region with the quality monitored by the quality making it possible to control fixing-setting value-adjustment, thus control has the mixing in the aggregative model of container-bottom compensation.

Example 9: gas and oil potpourri, the adjustment (not having premixed) of alloy

Fig. 7

This exemplifications set is by injecting the operation of the adjustment of adjuvant or alloy.

At this, regulate two characteristics by alloy: cetane rating and filtrability (filterability).Regulate the third characteristic (sulfur content) concurrently by mixing two kinds of base-materials, the third base-material is stopped that (block) is in fixed ratio.

Following table provides the value relevant to the sulfur content of three kinds of base-materials, filtrability and cetane rating.

Table 6: the characteristic of the base-material of example 9

The base-material being called as " base-material by stopping " injects with the constant ratio of 1.5%.

Sulfur content regulates in the setting value of 45ppm, and filtrability regulates in the setting value of-16 DEG C and cetane rating regulates in the setting value of 52.

As shown in Fig. 7 a-f:

The injection that Fig. 7 a shows in advance-hexadecane (pro-cetane) adjuvant be lowered until in the middle of mixing time cut off this injection, to reduce comprehensive cetane rating (Fig. 7 d), it is gently maintained at there close to its setting value.

Fig. 7 b shows filtrability alloy and injects, and has three peaks corresponding with the small oscillatory (see Fig. 7 e) in comprehensive filtrability.This represents the adjustment adjusted reactively.

Fig. 7 c gives the distribution of the base-material for regulating sulfur content.These distributions are very steady, and except mixing middle peak, it, as the result at the peak observed in the instantaneous sulphur measured value of Fig. 7 f, caused by discontinuous disturbance.

Comprehensive sulfur content is consistent with its setting value and do not have the discontinuous disturbance of mixed centre to affect in Fig. 7 f.

This example has set forth the following ability of system: by controlling component of mixture and passing through to inject multiple additives to control the various characteristics of potpourri, thus provide synchronous potpourri-Comprehensive Control.

Claims (22)

1. a method for the preparation of control n kind component mixture M, comprises:

When moment t=0, based on having the initial value B corresponding with following equation (1) ₀matrix the characteristic of the n kind component of middle set and estimate benchmark formula step (i)

$\frac{d{\hat{B}}_j^t}{\mathrm{dt}}=-{\mathrm{\&beta;}}_j\mathrm{Hu}(y_j-y_j^{\mathrm{mes}}),---\left(1\right)$

Wherein

● y _jfor the admixture characteristic of estimation;

● β _jfor strict arithmetic number, be the constant that convergence time is set, allow the speed of convergence idiocratically distinguishing estimation one by one;

● matrix H is positive definite symmetric matrices, has the normalized object ensureing to consider measurement-prediction deviation, allows constituent mass prediction deviation to calculate, thus supplying method convergence property; And

● be transposed matrix, wherein j is admixture characteristic index,

And make the characteristic of potpourri between predetermined minimum threshold and max-thresholds and/or, equal predetermined target value at least partially in them, and described equation is to the application of the true potpourri of component,

When moment t '=t+ Δ t, Δ t is the transition period between two Continuous plus iteration, based on the y of measurement characteristics of prepared mixture M ^mescorrection matrix step (ii) so that calculate with component of mixture estimate the correction matrix of characteristic corresponding new formula u, apply thereafter this new formula u to component to prepare mixture M, this step (ii) comprises following operation:

(1) the characteristic y of the mixture M obtained by being applied in formula that previous instant calculates is measured ^mes,

(2) correction matrix of the estimation representing component characteristic is derived thus

(3) determine newly to fill a prescription u, make the characteristic of potpourri between described predetermined threshold and/or, the m ' in them is individual equals described predetermined target value,

(4) this new formula u is applied to component;

At moment t "=t '+Δ t time, step (iii) is identical with step (ii), repeats this step (ii) during the whole preparation of component mixture in the same manner,

The feature of described method is that at least one additive correction by introducing at least one constraint condition corresponding with restriction, ordinal relation and/or equality constraint operates the matrix carrying out aligning step (ii)

2. the method for claim 1, is characterized in that, in order to correction matrix by equation (1) being replaced with new adaptation equation corresponding to rule and/or by adding additive term δ to revise initial value, that is, B ₀.

3. the method for claim 1, is characterized in that, revises matrix by the equation of the interpolation initial equation (1) being replaced with the additional function comprising peer-to-peer (1) that is:

$\frac{d{\hat{B}}_j^t}{\mathrm{dt}}=-{\mathrm{\&beta;}}_j\mathrm{Hu}(y_j-y_j^{\mathrm{mes}})+\mathrm{\&lambda;f}\left({\hat{B}}_j^t\right)---\left(1.1\right)$

Wherein

● f is nonvanishing function, its by selection with by the convergence of component characteristic estimated point to meet with limit, a class value of ordinal relation and/or at least one constraint condition corresponding to equality constraint;

● λ is weight coefficient, and it allows the return speed of the component characteristic estimated to be adjusted in the tolerance interval limited; And

● H is that diagonal matrix is so that the convergence property of ensuring method.

4. the method for claim 1, is characterized in that, revises matrix by initial equation (1) being replaced with the equation corresponding with the adaptation rule according to following equation

$\frac{d{\hat{B}}_j^t}{\mathrm{dt}}=-{\mathrm{\&beta;}}_{j}H\frac{1}{\mathrm{\&delta;t}}\underset{t-\mathrm{\&delta;t}}{\overset{t}{\&Integral;}}u({\hat{B}}_{j}u+y_j^{\mathrm{mes}})\mathrm{ds}---\left(1.2\right)$

Wherein δ t is window integral time, and s is the time variable of integration.

5. the method for claim 1, is characterized in that, revises matrix by initial equation (1) being replaced with the equation corresponding with the adaptation rule according to following equation

$\frac{d{\hat{B}}_j^t}{\mathrm{dt}}=-\frac{{\mathrm{\&beta;}}_j}{\mathrm{\&delta;t}}H\underset{t-\mathrm{\&Delta;}-\frac{\mathrm{\&delta;t}}{2}}{\overset{t-\mathrm{\&Delta;}+\frac{\mathrm{\&delta;t}}{2}}{\&Integral;}}u\left(s\right)({\hat{B}}_{j}u\left(s\right)-y_j^{\mathrm{mes}})\mathrm{ds}---\left(1.3\right)$

Wherein δ t is window integral time, and Δ is transfer delay, and s is the time variable of integration.

6. method as claimed in claim 5, is characterized in that, revises matrix by adding additive term δ to equation (1.3) and correspond to following calculating:

$\hat{B}{\mathrm{complete}}_j^t=({\hat{B}}_j^t+\mathrm{\&delta;})---\left(1.4\right)$

Wherein it is amended matrix and wherein vectorial δ meets equation δ * u=0, make prediction constant because of following equation:

$y={\hat{B}}_j^t*u=({\hat{B}}_j^t+\mathrm{\&delta;})*u---\left(1.5\right)$

7. method as claimed in claim 6, is characterized in that, define vectorial δ by direct algebraic manipulation or by the sequential optimization scheme under constraint condition.

8. the method for claim 1, wherein by the admixture characteristic y measured by during carrying out measuring process (ii) to the continuous coverage program preparing potpourri ^mes.

9. the control method as described in one of claim 3-6, it is characterized in that, before the preparation of potpourri when existence relates at least one compounding operation of at least two kinds of components, the new formula u determined during the operation (3) of modify steps (ii) is to consider the delay because the dead volume in the equipment in premixed region causes.

10. control method as claimed in claim 3, is characterized in that, by correction matrix during step (ii) realize replacing with variable U according to the new formula u of the adaptation rule of equation (1.1) by being used for, wherein U (t)=(U1 (t) ... Un (t)) ^t, at moment t, formula vector considers dead volume.

11. control methods as claimed in claim 4, is characterized in that, by correction matrix during step (ii) realize replacing with variable U according to the new formula u of the adaptation rule of equation (1.2) by being used for, wherein U (t)=(U1 (t) ... Un (t)) ^t, at moment t, formula vector considers dead volume.

12. control methods as claimed in claim 5, is characterized in that, by correction matrix during step (ii) realize replacing with variable U according to the new formula u of the adaptation rule of equation (1.3) by being used for, wherein U (t)=(U1 (t) ... Un (t)) ^t, at moment t, formula vector considers dead volume.

13. control methods as claimed in claim 6, is characterized in that, by correction matrix during step (ii) realize replacing with variable U according to the new formula u of the adaptation rule of in equation (1.3) and (1.4) by being used for, wherein U (t)=(U1 (t) ... Un (t)) ^t, at moment t, formula vector considers dead volume.

14. control methods as claimed in claim 1, it is characterized in that, determined new formula u at the end of step (ii) is obtained by the optimization method comprising series of steps, seek the solution of the minimum problem relevant with the minimum number of precedence constraints during this period, if be difficult to carry out about the whole issue of institute's Prescribed Properties, then increase the quantity of the precedence constraints considered in each step, until obtain the new formula u of the precedence constraints representing maximum quantity.

15. control methods as claimed in claim 1, for the preparation of the equipment of the potpourri of n kind component and adjuvant, it is characterized in that, for adjuvant to its influential admixture characteristic, control model is considered to add additivated effect d during the operation (2) and (3) of step (ii) according to following formula:

16. the method for claim 1, is characterized in that, revise matrix by adding additive term δ to equation (1) and correspond to following calculating:

$\hat{B}{\mathrm{complete}}_j^t=({\hat{B}}_j^t+\mathrm{\&delta;})---\left(1.4\right)$

Wherein it is amended matrix and wherein vectorial δ meets equation δ * u=0, make prediction constant because of following equation:

$y={\hat{B}}_j^t*u=({\hat{B}}_j^t+\mathrm{\&delta;})*u---\left(1.5\right).$

17. methods as claimed in claim 3, is characterized in that, revise matrix by adding additive term δ to equation (1.1) and correspond to following calculating:

$\hat{B}{\mathrm{complete}}_j^t=({\hat{B}}_j^t+\mathrm{\&delta;})---\left(1.4\right)$

Wherein it is amended matrix and wherein vectorial δ meets equation δ * u=0, make prediction constant because of following equation:

$y={\hat{B}}_j^t*u=({\hat{B}}_j^t+\mathrm{\&delta;})*u---\left(1.5\right).$

18. methods as claimed in claim 4, is characterized in that, revise matrix by adding additive term δ to equation (1.2) and correspond to following calculating:

$\hat{B}{\mathrm{complete}}_j^t=({\hat{B}}_j^t+\mathrm{\&delta;})---\left(1.4\right)$

Wherein it is amended matrix and wherein vectorial δ meets equation δ * u=0, make prediction constant because of following equation:

$y={\hat{B}}_j^t*u=({\hat{B}}_j^t+\mathrm{\&delta;})*u---\left(1.5\right).$

19. 1 kinds of systems prepared and control multicomponent mixture, comprise: want mixed component (1 for transmitting, 2,3) to the transmission channel (4 of main channel (7), 5,6), described main channel (7) are connected to the place (9) receiving potpourri, for controlling the device (10) of the flow velocity of component in each transmission channel, the measurement mechanism (11) of the representative parameter of the potpourri be just produced for continuous coverage in main channel, and for the calculation element (12) of the ratio that calculates the various components comprised in potpourri, be connected to the estimating apparatus (13) of calculation element, described estimating apparatus comprises the device by using the measured value of the admixture characteristic measured by measurement mechanism (11) to produce the estimation of component characteristic, described calculation element comprises the device of the ratio being calculated the various components comprised in potpourri by the mode of this estimation, thus obtain the potpourri with predetermined properties, the system is characterized in that, estimating apparatus (13) comprises for being introduced and the restriction at least one characteristic, ordinal relation and/or at least one constraint condition corresponding to equality constraint are to correct the matrix of the step (ii) of the method according to any one of claim 1 to 12 device.

20. systems as claimed in claim 19, it is characterized in that, estimating apparatus (13) comprises synchronous device, the delay that the dead volume in the region of premixed causes considered by described synchronous device, and described synchronous device is configured the equation (2) of the operation (3) of step (ii) to execute a method described wherein, U (t)=(U ₁(t) ..., U _n(t)) ^t.

21. systems as described in claim 19 or 20, it is characterized in that, it comprises the optimizer (14) being connected to calculation element (12) and potpourri target storage (15), described optimizer comprises the device of the formula u for optimizing component ratio, and described formula is determined with the potpourri target be stored in described memory storage (15) by calculation element (12) basis.

22. systems as claimed in claim 21, it is characterized in that, it comprises: at least one additive container (16) being connected to main channel (7) via transmission channel, is positioned at the downstream in the region of blending ingredients (1,2,3); For controlling the control device of the additive flow rate provided in transmission channel be associated with container (16); And be connected to the adjuvant injecting controller (18) of described control device, optimizer (14) and potpourri target storage (15), described adjuvant injecting controller (18) can consider the target that potpourri target storage provides, for adjuvant to its influential admixture characteristic y _joptimize the ratio of adjuvant, thus regulate the described individual features y of potpourri _j.